This is an interesting problem, with lots of answers, but I agree with Treez and Fvm early posts about reverse recovery transient.
As you know, the difference between SiC and Schottky is the zero reverse recovery time of the former - i.e. no current transient. Since it broke when you changed it, I would strongly suspect that is the reason for the problem. It sounds like you have concluded essentially this with "Rule 1".
Solving the problem without a replacement SiC diode is then somewhat harder. Adding some series inductance would be my first try, but then you need to make sure it does not introduce ringing and overshoot.
I wonder if another thing that might have the same effect is just dumb parasitic capacitance in the parts, and so trying a different Schottky diode might work? (My guess is no, since you probably have faster transients than other responders that have successfully used a schottky).
For a cluge, you could try stacking up 6 pcs 30 ohm 1206 resistors on the pads (one on top of the other).
Please let us know the resolution!