How do these gate waveforms look? Is the rise time too slow?

I have no idea what rise time is because scope time/division is not listed.  Oh, after noticing title saying 100kHz, I can then deduce scope is at 2us/div for first capture.  Listing both volts/div and time/div for all traces would be helpful.  Or amps/div for current.
Rise time is probably fine.  Some rise time is needed to provide dead-time between turn-off and turn-on.

Also, do you know why I sometimes get the noise on the primary current waveform at the switching transitions but sometimes not? In this case it might be relevant to fix the noise because it lines up with some ringing/noise on gate turn off.

Presuming UD2.7 or similar driver, phase lead does not function well at low current.  Once current builds, phase lead works better.  Phase lead makes switching at proper time slightly before zero current which reduces spikes.

1.) Question: Are there any pitfalls to this idea?

Sudden discharge of flyback transformer secondary due to spark gap can destroy transformer (or internal diodes).  Depends on internal construction.  Either add a Terry filter or have a few spare flyback transformers for experimenting.  Search for Terry filter and/or study this thread:
    https://highvoltageforum.net/index.php?topic=822.0
Above thread includes other cautions about unused flyback transformer pins, which might be relevant to your design.

3.) Question: Can I estimate the output voltage and current of the flyback accurately enough to do so, or should I try to measure it?

Can be estimated from simulation, but only if you know transformer characteristics (inductances, coupling factor, and saturation current).  May be easier/faster to measure.  At least you are starting with a ZVS/transformer pair that presumably is known to work together.  It is easy to end up with little power due to ZVS frequency too high or low for transformer (or other issues).

Hope your project is successful and a good learning experience.

Is this explanation correct?

Looks accurate to me.
Try simulating for a longer time period and/or reduce value of C1 to say 100nF.  Then you will see the need for D1.  D1 isn't needed for low duty cycles (short enable times), but is for longer times.

I ordered a few more globes and filled them with 15 torr and then 50 torr xenon. No toroid
behavior. I began to wonder if baking was the difference. So I build a sketchy oven and baked a
one liter globe at 350C for an hour. Filled it with 15 torr of xenon.

Baking under vacuum is the ideal glass surface degassing process.  Neon sign makers use a process they call "bombarding".  It's not quite full vacuum because 2-3 torr of added gas is needed to pass high current through the tube to cause the heating.  Not clear if the hot plasma inside helps degassing or hurts it.

But, in my hypothesis, and as the observations of others, the Magnetic field has a far greater effect than the voltage, or current moving through the coils.

As a potentially more approachable experiment, I'd love to see what'd happen with drive frequencies outside of the now-customary 10-15MHz range.

A relatively high electric field is needed to start internal xenon glow discharge.  A lower field and higher current maintains the discharge (torus).  The starting electric field is usually capacitively coupled to xenon through tube wall, from a starting wand or from coil voltage.  Sustaining electric field is almost all induced by the AC magnetic field, which is why the discharge is a torus.  Not clear if the magnetically-induced electric field is ever high enough alone to start discharge.  That's something I hope to experiment with some day, using a single-turn coil (high current at relatively low voltage) to minimize capacitively coupled electric field.
Frequency will be a great variable for experimenting.  Lower frequency will require more current (stronger magnetic field) to induce the same electric field.  That stronger magnetic field should push the torus farther from coil due to stronger magnetic repulsion.  Farther from coil will reduce electric field.  May result in more self-extinguishing and restarting.  I expect high frequency will be most efficient at generating a stable torus close to coil.
Of course, buoyancy of of the hot torus also causes it to rise.  One of the videos shows the significant behavior difference between coil on top vs bottom of xenon-filled glass sphere.  With coil on top, torus is stable and closer to coil.  Don't recall which video shows this.

1) In the video I've attached I noticed the OCD triggering (the red light) more for small arc lengths than for long arc. Is this abnormal or is it because of the buildup current required to extend the arc which the brings the coil into tune because of the reduction of the resonant frequency? Should I leave it as is or does it require better tuning?

Notice in your video that the short arcs occur on lower notes.  Arc path from previous note cycle (previous enable pulse) has longer to cool before next enable pulse.  Cooler path requires more voltage to ionize air again.  Primary current hits OCD before secondary voltage has been high enough for long enough to grow arc longer.  Yes, you are correct: Once arc grows somewhat long, secondary frequency drops to better match primary frequency, allowing more energy transfer to secondary without exceeding primary current limit, further extending arc length.
Tuning primary frequency slightly higher will increase arc length for low notes, but likely reduce arc length for higher notes as secondary frequency drops below primary due to arc capacitance.  You can test to see which behavior you prefer.  No one "right" answer.
Your coil has a couple similarities to my DRSSTC: Secondary impedance is below typical 50k, and coupling factor is on the low side due to tall skinny secondary design.  Both tend to exacerbate above tuning tradeoff.  If mechanical construction allows, you could try raising primary slightly to increase coupling.  Higher coupling transfers more energy to secondary for given primary current and detuning.  If coupling is too high, secondary racing sparks become a problem.  I had to drop from my original 0.147 to 0.141 due to racing sparks (primary lowered from 50mm to 25mm above bottom of secondary).
Without remaking secondary, only option to increase impedance is smaller top load.  But that itself reduces performance, so not recommended.

2) The primary connection lead(the thick red wire) passes by close to the driver enclosure(the yellow box) which led to it heating up after long runs. I thought this won't be the case if the enclosure is grounded. Is it true and its not grounded properly? Or should I just increase the distance between them?

Likely issue is induction heating, not grounding or other electric field issue.  Steel (ferromagnetic) housing heats very efficiently due to local AC magnetic field.  Either move cable away from enclosure or change to an aluminum (or copper) enclosure.  Or add an aluminum partial enclosure around that portion of steel enclosure.
Did the entire enclosure heat up or just part near wire?  Looks to be far enough from primary coil, but induction heating from primary coil's magnetic field is also a possibility given how easy it is to heat steel.

Great accomplishment!  Thank you for sharing.

Seems to work fine with zero hysteresis in the simulator, might this cause some problem in practice?

Likely fine in practice.  Same as infinite gain linear feedback.  Resulting buck converter frequency is controlled by total delay around loop.

Looking into it, the capacitance change with voltage in ceramic capacitors seems a lot more significant than I had previously realized. Obviously, these Chinese caps don't have a specification on capacitance with increasing voltage or even what dielectric is used, so it seems safe to assume it's pretty bad.

Capacitance vs. voltage specifications are rare for almost all ceramic capacitor manufacturers.  Some of the larger well-known companies have started publishing typical curves for their parts.  Varies widely, even for the relatively cheap ones.  One supplier's parts may drop by 90%.  Another similar-looking part from another supplier may drop only 30%.  I saw one report here saying the Y5V dielectric parts they'd purchased measured as only -30% at rated voltage.
I'd suggest using 40kV caps rather than series-connected 20kV caps.  With series pairs, bleed resistors are needed across caps to keep charge equal.  Oil circulation currents can be significant, causing the imbalance.  As was suggested by huntergroundmind, insulating baffles will reduce oil circulation, but probably not enough to avoid need for resistors.
Only Y5V 40kV cap I see on EBay is 10nF:
    https://www.ebay.com/itm/204483870595
Another option to consider is film capacitors such as these polystyrene dielectric parts:
    https://www.ebay.com/itm/225014970693
I've purchased some of these before.  They should work quite well for voltage multiplier use.  Capacitance is constant over voltage.  They are not good for repeated sudden discharge such as Marx generator, but that doesn't matter for you.

Are there any other considerations here? Increasing the capacitances to 1nF in the simulation significantly reduced the output ripple (See result3.png).

Increasing early-stage capacitance will increase output voltage for a given input voltage due to lower ripple.  Will be more pronounced at high load and with high parasitic capacitance.  I think the optimum distribution for 4 stages is 4x, 3x, 2x, 1x for the stages, where x is capacitance of final stage.  Of course, no need to hit exact ratios.  Any change to increase capacitance of early stages helps.

Using multiple diodes in series seems like the only option if I want 120kV using a four-stage multiplier. I was unable to find any diodes with a higher voltage rating than 20kV. Does anybody know of some that arent extremly expensive?

May work fine.  On Ebay there are 30kV and 40kV diodes available.
    http://www.hvgtsemi.com/picv_994.html
is one 40kV part available from a couple Chinese EBay stores.  No personal experience with these parts.

I tried first with 2pF of capacitance parallel to the diodes and the output couldn't even reach 65kV. Estimating the capacitance as two parallel wires 5cm apart, 2cm long, and 1mm in diameter using a Relative Permittivity of 2.2 for mineral oil comes out to ~268fF. The diodes claim a Max Virtual Junction Capacitance of 1pF, but the Diode model already includes that. I decided to add another 1pF parallel to the Diodes just to be on the safe side, and it didn't cause any problems even at 125% load (See result5.png).

Actual stray capacitance depends on geometry.  For a crude guess, something like 0.5pF/cm (50pF/m) of multiplier length presuming in oil in a plastic (insulating) housing.  A metal housing will add capacitance.  If that ends up being closer to 2pF per diode, higher early-stage capacitance will help get voltage back up.

Good luck with your build!

I know it is a balancing act, so is 15 be good...?

Here's my tutorial on GDT construction.  Reply3 shows how to calculate needed turn count.
    https://highvoltageforum.net/index.php?topic=1854.msg13949#msg13949

I've been tinkering with a setup where M3, D11, and L3 form a buck converter without output smoothing.

Yes, that works well.  Great idea.  BTW, I suspect L3 could be much smaller value.

The duty cycle at the gate of M3 flips between two fixed values depending on how the output high voltage compares to the setpoint voltage.

I think it would function fine with the two fixed duty cycles being 0% and 100%.  Would simplify circuit considerably.
Either way, if the flipping frequency is within audible range, may make some audible noise (vibration of magnetic components).  May not be enough to annoying.

R6 acts as an output current limiting resistor,

Do you expect sudden discharges such as an arc from HV to ground?  Probably a good idea to include the resistor just in case, even if intended load has no sudden shorts.

The feedback network, made up of R8/R9, attenuates the output voltage, which is then scaled by U4 so that 150 kV is around 4.9V. U5 compares this feedback voltage to the setpoint and outputs either ~0.5V or ~4.5V. Then, this voltage is compared to a triangle wave to create the PWM signal for the buck converter.

If you do keep the ramp generator (PWM other than 0% and 100%), why not linear feedback (duty cycle proportional to error voltage)?

Check out the attached pictures for the schematic and simulation results.

Great simulation.  Kudos for simulating before constructing.

Are there any glaring problems or difficulties with building this design that I might be overlooking?

Just make sure V2 turns on before V6.  Then verify experimentally that power from V2 through R3 and R4 is sufficient to start low-amplitude oscillation.  If V6 turns on first or simultaneously, ZVS oscillator may not start, resulting in very high V6 current and fried FETs.
Of course, all the normal HV insulation requirements (oil immersion or whatever).

Great project!  Looking forward to seeing your progress.

I have one large area gdt wound following instruction on this site, it has one primary and 4 outputs as in the picture.

If not using a pulse-skip driver needing two GDTs, one is fine.  However, it is best to wind the one with four twisted pairs, not just three.  Primary is four parallel windings, one wire from each pair.  Secondaries are other winding of each pair.
If you have already made two GDTs with two twisted pairs each as in my tutorial, that works just as well as a single GDT with four twisted pairs.

Now that I've learned more I'm realizing Dave's wisdom (thanks!)

Thank you for the compliment!  But please don't hesitate to question or challenge my "wisdom".  I do make mistakes.

I think I'm going to stick to inductive pusher designs for a while instead of worrying about a linear motor.

Definitely simpler to start.  However, remember that pusher projectiles are more efficient when short, opposite of what you want for ballistics.

I will also have to do math to calculate the clamping force!

I haven't used clamped thyristors before.  However, AFAIK clamping force is primarily to improve heat transfer.  For your low duty cycle use, just enough force to make a reliable electrical connection is likely sufficient.

One thing I'm wondering about that I might need to do an experiment with is: does a thyristor block negative voltage?

Some analog circuit simulation (LTSpice or other) would help in thinking about current and voltage, especially through inductors.  Ideal inductor has current lagging voltage by 90 degrees.  Most thyristors (other than TRIACs) block reverse current.  In other words, they allow reverse voltage without conducting current.  However, be careful with high-speed thyristors intended for pulse discharge.  They often handle only small reverse voltage before being damaged.  IGBTs are similar in that respect.  They block only small reverse voltages.  Many IGBTs packages include an internal diode.  Internal diode prevents significant reverse voltage by conducting reverse current.  If you are using a pulse-discharge thyristor or an IGBT without internal diode, an external diode is needed to prevent device damage.

On a related note electrolytic capacitors presumably won't work for the inductive coilgun since they won't like the negative voltage

At least won't work efficiently.  A diode can be used across an electrolytic capacitor to prevent significant reverse voltage.  But then inductor current decays slowly.

but I think the IGBT will transmit that whereas the thyristor may not?

Here's where circuit simulation will help.  The same positive current direction that discharges cap will "discharge" it through zero to negative voltage.

a reluctance coilgun which I bought some 480v electolytic capacitors for.

My reluctance coilguns are all low power for kids to use.  (One down to 20V so hand wire contact is sufficient to fire.)  They all use electrolytic caps.  My coils have enough resistance to be critically damped, avoiding capacitor reverse voltage.  This is not efficient, however.  Nor is the above solution of diode across capacitor.  Ideally coil current would end when projectile is at center of coil.  Anything that slows current decay causes reverse force as projectile proceeds past coil center.

I've found bigger film capacitors but they are big and scary and I need to practice safely discharging smaller ones and generating voltages to begin with before I mess with those.

Good to be cautious.  Your 45uF 800V caps are in the energy range of defibrillators.  Even that can be lethal.  As energy increases (ie. coin shrinkers etc.), one mistake is the last one you will ever make.

Have fun!  And of course do so safely!