If there is a possibility that an external force (inertia does not count!) can rotate the motor to higher RPM than the bridge, given its DC bus voltage, is ever able to, only then is back-EMF able to generate voltages too high. For this, adding large TVS diodes to the DC bus, that can burn that actual mechanical energy helps, but is expensive. Forbidding (by documentation) such external fast rotation is usual.
Additionally, a broken-by-design control side can cause high DC bus voltage even with lower RPM, i.e., the motor is regenerating (in this case, inertia does count); then the bridge is able to boost up the fairly low back-EMF voltage at that RPM, so that it exceeds the bridge transistor ratings. The cure is to fix the control so that once the bus overvolts, all FETs are instantly turned off; hence boosting stops, and the DC bus only sees the rectified back-EMF voltage but no more.
But, my guess is, this has nothing to do with back-EMF, but everything to do with excessive ringing because of insufficient DC link bypassing and layout. Need to see the layout. RC snubbers may be needed, but bypassing and layout needs to be the first thing to be perfected. Then it's highly likely no RC snubbers are needed after all.
What comes to jmelson's suggestion, I've never used diodes in parallel with MOSFETs in motor controllers. I think the claim about the MOSFET body diodes being "very slow to turn on" in unsubstantiated. MOSFET body diodes do have larger Qrr and higher Vf so paralleling with a schottky can bring losses down very slightly (most of the gain can be had by just finetuning dead times), though, but I'm almost 100% sure not using an extra diode isn't the root cause for the problems seen here. It doesn't hurt to add them, but it shouldn't be #1 in the list.