How to dampen a royer oscillating power circuit
The pushpull Royer ZVs osc that you have will make big peak drain voltages when run off rectified mains .The peak DS volts are Pi * Peak DC supply volts .Remember that the peak of the rectified mains could be 1.414 * 230 if the load is light.The tailing of the IGBTs does distort the DS voltage waveform tending to make the peak higher .When you are heating your workpiece the currents flowing in the hot metal are relatively sinusoidal .The HF tank is having sinewave current drawn out of it .The current in your DC feed choke will be relatively constant during the AC cycle .This is because the choke is chosen to have relatively high impedance at the switching frequency and of course low DCR .The self oscillating switching action of the pushpull IGBTs feed the tank with pretty much a square wave of current at the resonant frequency .This means that some more distortion on the tank voltage is to be expected.Standard 1200V IGBTs are looking very borderline here .I have Always fed my ZVs ROYERS with a buck convertor .I measure the DS volts with a simple Diode peak detector and feed it back into the buck convertor control .I have used S trap and used Peak current mode and even voltage mode.You can use anything that has fast current limit and is stable into a relatively low output capacitance .If C out is huge its energy stored at bucked down rectified mains will be capable of blowing the IGBTs anyway despite having fast current limit on the Buck. C1 is under a lot of stress .Its not just the voltage but the frequency .The voltage rating of most caps falls with increasing frequency .This is due to heating caused by High Ac currents heating up due to ESR and dielectric losses .It is common to see many caps in parallel to reduce ripple current heating .     Please use an isolation transformer if you start setting all this up .