How is drive connected? What is ground in this circuit?
Resonances can usually be traced to a combination of known capacitances and/or inductances; xavier's note for example.
You may find it's better to use a TVS, than a dV/dt snubber. If nothing else, the dV/dt snubber needs to have a capacitor much larger than the nearby capacitors, so that the peak voltage is limited proportionally.
1N4007 is wholly unsuitable here. It turns on much too slow, and isn't rated for enough peak current, anyway. 1N5404 probably the same.
I've demonstrated a small current limiting switch of broadly similar design, which is capable of drawing up to 110A peak, turning off in 3 microseconds (while offering excellent lifetime from battery power). To handle inductive loads, it has an RCD snubber (470nF, 1 ohm and, B560 schottky diode I think?) in parallel with a TVS (SMDJ48A, with the transistor being rated for 80V and the actual peak drain voltage being 65V or so).
Regarding stray inductances, we can calculate limits for the transistor and snubber. Say the transistor is capable of turning off in about 200ns (typical for an IGBT, though if it's a newer type, it may well be significantly faster than this!). That means your goal of 200A peak, in 0.2us, gives a peak current slew rate of 2000A/us (or probably a bit more than this, in the middle of the falling edge, since it's a curve, not a trapezoid). If the transistor is rated 600V and the supply is 300V, we need to limit peak induced voltages to less than 300V (300 + 300 = 600V limit).
Inductance is defined as the ratio between voltage and rate of current, i.e., L = V / (dI/dt). Or equivalently, the ratio of integrated voltage, i.e. flux (V dt), to change in current (dI). 300V / (2000A/us) = 0.15uH.
This translates to a physical length, given some known geometry. For stray wiring, the factor is around 1/4th. The ratio comes from the permeability of free space, mu_0 = 1.257 uH/m. 1/4 is 0.3uH/m, so we might guess a maximum distance between transistor and snubber (preferably a 300V TVS in this example) of 0.5m.
If the transistor is faster and the current is larger, or the voltage limits are more restrictive, all of these measures are reduced proportionally. For a 30V overshoot, we need less than 5cm; for a MOSFET switching in 20ns, we need less than 5mm -- and that includes component lead length and body length!
Tim