Ok, here are my comments. When you create your responses I ask that you please answer my questions/concerns one-by-one in an itemized list with matching numbers. This makes sure that nothing gets left out.
1) My first concern is that you're trying to drive opposite legs of the GDT with two outputs that are in-phase with each other. U5 and U6 are the same device, they're being fed the same input signal (from your feedback circuit), and their outputs are tied across two sides of the transformer primary. They're going to be fighting each other, and it's amazing that it's even working at all right now. One of them needs to be inverted (look at the UCC27321 inverting model to complement the UCC27322 non-inverting model). Was thinking you had this already. Did you change it? Is the schematic wrong, and you ARE using a '321 and a '322?
2) Second concern is the DC blocking capacitor(s) C5 and C6. What is C6? It's labeled "000".... 1uF is probably fine for C5, but I'm going to ask you to probe the GDT primary winding with your oscilloscope. If it's ringing due to the capacitance and the inductance of the GDT primary (which I suspect it is) you will need a damping resistor sized to damp the oscillations. This resistor will go in parallel with the capacitor, but you will need a smaller value capacitor (0.01uF, perhaps) in series with it to avoid creating a DC path. If you need a drawing to understand then let me know.
3) Make sure you have ~10uF ceramic capacitors located directly on the supply pins of the MOSFET driver chips. Each chip needs its own capacitor. These capacitors act as reservoirs and ensure that you can supply enough current to drive the MOSFET gates at the high frequency. I see you have 100uF on one of them, but that looks like a polarized capacitor (probably an electrolytic) whose ESR/ESL is much too high to supply the current to the MOSFET gates quickly. I'm not saying remove it, but I'm saying you definitely need ~10uF capacitors directly on the driver supply pins (as close as possible to them).
4) What is your GDT ratio? What are your transistor specs? (You may have mentioned this already but I need to know the current state of things - I know you bounced back and forth between IGBTs and MOSFETs for a bit). It is very important that the drive voltage is high enough to "slam" your transistors into saturation, otherwise your switching times will be off and you will likely draw excessive current from your driver chips (causing them to heat up).
5) How many channels does your oscilloscope have? Last I knew you weren't using a real one. It's cases like this where it would be really nice to have a real four channel scope. I need to see the switching waveforms G-S of each transistor so that I can see the timing relationships. Having all four waveforms on a single screen would be immensely helpful, or at the very least two complementary waveforms (two high-side transistors, then the two low-side transistors, perhaps).
6) The input capacitance on your LM7805 should be closer to 0.33uF and your output capacitance should be closer to 0.1uF, according to the 7805 datasheet. Not a huge concern and probably isn't causing any trouble, but best be on the safe side. It may prevent unwanted oscillations from the regulator.
7) Your 74HC14 should have a 0.1uF decoupling capacitor across its supply pins.
8) Since your feedback is fed directly from the current transformer I highly recommend placing a current-limiting resistor just before the input to the first 74HC14 gate. Otherwise you risk damaging your IC.
9) What happened to your primary coil circuit? It is not in this schematic. Do you still have a DC-blocking capacitor in series with it?
10) This is just me being picky and really has no bearing on the circuit, but the symbol for D10 shows it as a Zener but it is a Schottky. Just so you know....
Take as much time as you need to put together answers for these comments/questions. If you change the circuit, please make sure to provide an updated schematic next time you post. It is very important to keep it up to date.