Sounds like primary resonance test was w/o CTs and matches JavaTC, so no need to repeat that.

Correct, I think the primary resonance measurement is reliable.

One other less-likely possibility is an unwanted resonance of on-board bypass capacitors (snubbers) and lead inductance to bulk caps.

Very interesting, an unexpected resonance is something I need to investigate. It would explain why even when running with external feedback the output is really poor since the primary is resonating way above the resonant frequency of the secondary at about twice the drive frequency. I actually have left the RC snubbers unpopulated on my bridge PCB and only have the DC link caps and TVS diodes installed for transient control. Does this rule out that possibility then?

I currently have no MMC bleed resistance installed and I’m considering trying to add that to see if it changes anything.

The ground wire is visible in the second photo passing through the secondary CT. I am already using a variac on the bus input. The testing has all been done well below full bus voltage.

why not use lower permeability material in the first place.

Because there are few such materials, and none AFAIK with sufficient saturation flux density and low hysteresis.  That is why lower permeability materials are artificially constructed by adding air (or epoxy...) gaps.

A Hantek USB scope I bought a couple of years ago, a Peaktech 3440 and one of those cheap LCR T7 Multi transistor testing tools.

For measuring possible CT, LCR meter would be easiest, though might be a problem if LCR meter frequency is too low.  10kHz might be OK.  100kHz would be better.  Scope and signal generator will be more reliable.
Either way, I'd wind 10 turns of wire around CT core, through the hole where one wire normally passes.  Check pins for continuity.  Presumably only one pair will connect.  For LRC meter, measure inductance of pin pair and of 10-turn winding.  Turns ratio will be sqrt(inductance ratio).  For scope, connect signal generator to pin pair and run at ~100kHz.  Scope waveform across pin pair and then across 10-turn winding.  Voltage ratio is turns ratio.  Make sure signal generator output has no DC component.  Add a series capacitor to make sure.

CTs aren't difficult to make if you have cores.  Line input common-mode choke cores generally work well.  Other salvage cores are not likely to be good.  Large EMI filter beads can work as CT cores, but will require more testing to verify.  Same core options for GDTs.

Someone else can talk about possibility of very high anode voltages in your VTTC fault case.

You might get some comfort if you had a dosimeter than can indicate exposure to ionizing radiation.
The 1950's era CD V-138, with full scale range of 200 milliroentgens, is easy to buy online.
https://www.orau.org/health-physics-museum/collection/civil-defense/cdv-instruments/cdv-138.html

Here is video of one specimen getting zapped by a dental x-ray generator.