BWAHAHA RCA cables, is that what they are!

But anyway yeah, you've got a good probably 300nH supply inductance, about 100 of which is between the transistors. Not clear if you have other ground paths between DC link and control.
Check the DC and transient voltage limits on that gate driver, particularly between the bootstrap common and VSS. Consider switching speed i.e. dI/dt with respect to that inductance.
Oh yikes, and a big fat output cable running right over all the control signals, that can't be helping either.
If you're looking for a slam dunk:
Make a 4-layer PCB that screws onto the transistors.
Put DC+/- on inner layers.
OUT1 and OUT2 on bottom.
Gates on top.
OUT1/2 can be taken out to screw terminals without having to cross anything. Use an inline current transformer maybe.
Likewise DC+/- can be poured in the middle and taken out to screw terminals without having to overlap the drivers.
Use ground plane under the drivers. Probably use somewhat larger capacitors, too.
Use fat wide pours for all transistor connections, including the gates.
Add a few film caps to bypass the supply, 1-4.7uF, e.g. TDK B32672 family.
Keep the Kelvin gate connections, don't short the two emitter terminals together.
Put the gate drivers along the board edges, within a few cm of their respective transistors.
This at least has the possibility of getting stray inductance down below 20nH, and eliminates the resistance and inductance of the gate driver cables. You can use smaller gate resistors (mfg recommends 2.2 ohms; plots up to 10 ohms). The board cost will be only a few times what your existing control board was, probably the same or less if you include the labor of cutting and shaping the bus bars.
Can also consider TO-247 or TO-264 transistors, soldered into the board. Cheaper than SOT-227s. Tied to planes at the leads, the stray inductance is about the same either way, no performance loss. Obviously, if you already have a tube of the latter, this doesn't help much, that's fine.
Tim