Problem with mosfet in H-bridge
Check your voltage with a scope on the FET side of your filter.  (use a x100 probe and be careful).  You will likely be seeing excursions above the FET breakdown voltage of 500 volts, and your FET is doing what you want your TVS diodes to do.

Your real issue is that with reactive loads (capacitors or inductors), the current and voltage are 90 degrees out of phase.  This means that during part of the sinusoidal waveform, your current will be flowing in the opposite direction to that experienced with a resistive load.



During this period, the current is flowing "backwards" into your power supply.  This can cause your problem.  For example, with an inductive load, if your DC supply cannot absorb and dissipate this energy, your input voltage will rise until the current conducts somewhere (in your case the FET breakdown voltage or reverse VGS).  These are not small currents.  Although the TVS diode will work in theory, it is not your best solution because it is inefficient; you are storing energy in your inductive load, the pulling it back to heat up your TVS diodes.  

If you want to run reactive loads, you will have to do some power factor correction.