Thefore I think there is something bad with the chip

Unless the chip is counterfeit, a bad chip isn't too likely.  Possible that ESD partially damaged an input.  My second guess would be interconnect parasitic inductances, given breadboard construction without ground plane.  But core saturation is still possible, or excess leakage inductance.  Random unknown transformers aren't that likely to work.  If you have access to an impedance bridge or at least LRC meter, measure winding inductances and leakage inductances.  Then you can make a Spice model.  Measure saturation with a capacitor ring-down test.  (Charge capacitor, then discharge into transformer winding while scoping voltage.)  Gapped ferrite cores have a relatively sharp saturation knee.  Reasonably obvious on scope trace.  Easier to explain after you see traces.  If entire ring-down waveform is sine-wave, then increase voltage or capacitance.

I did end up damaging a FET running it at 80V. Interestingly, the FET still works, but it acts as a 60 ohm resistor when it's switched off.

Most FET failures are closer to a short, under 1 ohm.  I have occasionally seen such resistive shorts.  No experience with these cascode SiC FETs.  Low voltage silicon FET may have failed partially.  Is the 60 ohms linear with voltage?  Silicon FET damage would result in resistive at low Vds (ohm meter measurement) becoming a constant current at higher Vds (15V and up).

My first guess as to cause is poor thermal contact from package under die to heatsink:
https://highvoltageforum.net/index.php?topic=2191.msg16147#msg16147

Purchased a TA-40CS ultrasonic plastic spot welding transducer with aluminum horn.  Input is via what looks like a deep BNC connector.  Turns out to be SHV connector, generally rated to 5kV.  So far I've been using no more than +-1kV peak.

Anyone have specs for these?  There isn't even a brand listed on transducer, only model and serial numbers.  Model number hints at 40kHz.  Lowest resonant frequency is 12.6kHz with overtones to at least 130kHz.  40.2kHz resonance is narrow-band (high Q), appearing to be intended operating frequency.  Drops towards 40.0kHz as transducer warms up.  One reason for so many overtones and low minimum frequency is that the horn with this transducer is a full wavelength long rather than the usual half wavelength.  (BTW, recently purchased another transducer/horn shown in video below.  It is normal half-wavelength.  Haven't measured resonant frequencies yet, other than to know that it works well at 40kHz.)

Big question is how hard to drive the transducer without damage.  I've found a bit of general information about ultrasonic welding converters.  One table listed typical transducer output amplitude as 8um P-P for 40kHz transducers.  Used a microscope with strobed LED illumination to measure displacement.  I'm running 6-7um for a bit of margin.  Displacement at horn tip is ~20um.  This is called horn "gain" by industry terms, about 3x here.  Really just coupled mechanical resonators increasing amplitude by 3x and reducing force by 3x.

Measuring impedance vs frequency of transducer around 40kHz, I made an electrical model covering only this one resonant frequency.  Standard topology for crystal resonators (high-Q series resonant circuit paralleled by capacitor).  Resonant series resistance changes with mechanical load, increasing ~10x as plastic melts and becomes viscus.  Frequency changes a bit too.  Displacement is proportional to voltage across small series-resonant capacitance.  For fixed frequency, current tracks voltage.  I made a 3-winding current transformer.  Main 1-turn primary monitors transducer current.  Second 20-turn primary is driven by a capacitor roughly 1/20th of transducer parallel capacitance to cancel that part of transducer current.  CT secondary tracks transducer resonant current which tracks displacement.



Added a parallel L and C to CT burden resistor to reject harmonic frequencies.  Third harmonic of 40kHz is close enough to an overtone that my control circuit would occasionally lock to that instead of fundamental.  Occured when fundamental was heavily damped due to mechanical load.

Built this from the H-bridge laying around from this thread:
    https://highvoltageforum.net/index.php?topic=1324.msg9886#msg9886
Wound a new GDT for lower frequency.  Added common-mode chokes to GDT output; unlikely to be needed here, but perhaps for some future use.  Output feeds a 19:47T gapped ferrite transformer.  Gapped because some parallel inductance helps with H-bridge ZCS at max load.  Transformer output drives transducer through an inductor.



Finally, a video showing the setup and use:
    />
I've had best success with welding polyethylene and polypropylene, even mixed PP to PE.  Those two melts don't mix.  Mechanical interlock of melted bits makes a reasonable strength joint.

I am confused because I am using self oscillation.

Just mentioning that your experience was matching normal w/o self oscillation.  Appears for some reason self oscillation isn't helping force upper pole frequency.

So upper pole is going to be a bit above that?

Yes.  How far above depends on coupling (and on primary frequency).  High coupling (generally good for QCW and ramped coils) makes upper pole frequency higher and lower pole frequency lower.

That is what I want to tune my primary for, slightly above 462kHz?

If self oscillation doesn't work to allow lower primary frequency, then yes.

If that is the case then I also want to run the oscillation mod at or around that frequency as well, right?

If using self oscillation only to start oscillation and not to force upper pole operation, then yes.

Self oscillation can cause upper pole operation even with primary frequency lower than secondary frequency.  That's what my QCW coil does.  However, I think that works best when primary-to-secondary coupling is high.  My QCW coupling is higher than most at 0.7.  I think one or two other forum members have had success with self oscillation forcing upper pole with coupling around 0.4 or 0.45.  Not sure if anyone has tried with lower coupling than that.

5 turns on my primary and 20-30nF for my resonant cap. The issue doesn't seem to show up when I am above the resonant frequency of the secondary. I check my primary output and CT feedback frequency if it is to high I add a small amount (2.2nF) and remeasure, I see the primary frequency drop accordingly but as soon as I get close to resonance (coil with topload = 462kHz) the primary switches to a much lower frequency (around 350Khz), much lower than what adding a single 2.2nF cap would cause.

This is normal behavior for standard drivers without self-oscillation.  If primary frequency is slightly above secondary, oscillation is at upper pole.  If primary is slightly below secondary, jumps to lower pole.  Self-oscillation can help force upper pole operation, but only if primary frequency isn't too far below secondary.

I am missing where the post number is, can you link it for me?

Look at the top of each post to any thread.  There's a line such as this one from your last post:
     « Reply #46 on: Today at 10:18:40 PM »
I'm referring to reply 37 of this thread, 9 posts before your above one.  It's in page 2 of this thread.  In case that isn't clear enough:
    https://highvoltageforum.net/index.php?topic=2651.msg20288#msg20288

Only one non-critical detail comes to mind:  D6 and D7 are not very effective since there forward voltage drop will be similar to that of IC7's internal diodes.  Generally best to either use schottky diodes (ie. BAT54) or to add a small resistor in series with IC7 input.  However, IC7 may handle input current without functional issues, especially since it is a single gate without adjacent circuitry to be bothered by substrate current.

One other thing, what would be a good core material for a current transformer at 8+ MHz? I'm thinking some NiZn ferrite but i'm not sure.

Yes, NiZn ferrite is the best option AFAIK.  That's what I use on my 13.56MHz HFSSTC for GDT core.

Can you see any improvements I could make?

Of course there are many ways to achieve roughly the same end result.  Building what you have is a great way to learn even if there may be simpler options.

One variation to consider implements cycle-by-cycle duty limiting.  Make timing capacitor discharge a controlled current rather than rapid.  If the interval between interrupt input pulses is short, cap isn't fully discharged, so will require less time to charge to threshold, shortening enable pulse width.  Discharge current would need to track charge current, such as complementary current mirrors with POT between the two mirror inputs.

Is there a better way to limit the max output voltage from the op amp without affecting the rest of the circuit?

Limiting opamp integrator (or low pass filter) output voltage isn't easy when + input voltage varies as in your circuit.  If + input voltage is fixed, then a diode (or diode in series with shunt regulator or multiple diodes or LED for higher voltage drop) from output to - input works for clamping.  You could change to have fixed + input and adjust bias current into - input.

Scope traces need to be defined to be of use.  What signal is on ch1 and on ch2?
Most scopes can be set for probe scaling.  If using 500x probe, set scope for that.  Then displayed volts/division will be correct.
Scope vertical channels are set for AC coupling.  DC coupling is better for most measurements.
What burden resistor is on scoping CT secondary?
UD2.7 has two CT inputs.  Do you have a third CT for scoping?

I think i'm satisfied with this for now. I want to try a PLL version in the future, so you may see a thread about that soon.

Looks good.  Always nice to see projects finish working well.
I suspect a PLL version will avoid need to tune primary as arc grows.  Instead frequency will drop to match arc loading.  Same goes for any other way of tracking frequency such as the much more common self-oscillating versions.

Currently, I have it about halfway seated. If the goal was to reduce that dip as much as possible I think where I have it set now is it.

Looks good, though I'd consider setting it for slightly more phase lead still (slug farther in).

The arcs seem to all be splitting, usually into two from the breakout. I have yet to get a single straight arc. In an effort to get straighter arcs I am going to try and increase primary impedance by winding a new primary. Currently I am using high MMC value with few turns. I am going to try and reverse that to see if I can slow arc growth down a bit to reduce branching.

Sounds like a good plan.  I'm certainly no expert on making single straight arcs, but slower ramp rate fits my limited experience.
Edit:  Another change to try is increasing breakout point length.  Found with my QCW coil that if breakout was too short more voltage was required to start arc (as expected).  That higher voltage caused immediate branching as arc grew rapidly initially.