You have already C7 and C8 as low ESR, high current film capacitors. Why would you need additional snubber capacitors parallel to the main bus capacitors?
Assuming that the high frequent output current is mainly sourced by C7 and C8, each capacitor is loaded with a half-have, corresponding to 23,5 A Irms each. You most likely need a parallel circuit of multiple high current capacitors (e.g. Kemet R73, Wimi MKP10) to handle the current.
Regarding capacitor sizing, one option is to establish a series resonant converter with C7||C8 and transformer leakage inductance.
Bipolar versus unipolar gate drive, I just wanted to mention that high current IGBT are ususally expected to use bipolar gate drive. This doesn't mean that unipolar isn't feasible, but you actually need to optimize switching parameters, not just copy and past a gate driver circuit from a low power application. I also think that HCPL3120 is on the lower edge of required gate current.