How to properly snub transient spikes from a transformer and prevent switch mode power supply burn out
The LTC3631 is a low-power converter (100mA only) so there are a few ways one could hypothetically save the device from surges.

The easy solution is adding some clamping on the primary side of the transformer to limit any surge energy coming in - a MOV from line to line will shunt any high voltage energy away from the transformer. A small series resistance would also help limit the surge energy, and wouldn't be excessively lossy since the regulator draws such a low current. Safety-rated X-capacitors from line to line may also help with smaller surges (also sometimes called 'fast transients') - just don't forget to put a resistor in parallel with them that would discharge them within 30 seconds, for safety reasons.

Clamping also works on the secondary side. You could add a small resistor in the positive feed to the regulator, then put a TVS in parallel with the regulator (between the positive feed and ground). The TVS would clamp the voltage to a safe level and the resistor would limit the TVS current. Again, it would burn some power all the time, but the regulator isn't high-power so the losses should be manageable.

Local capacitors directly at Vin and Run going directly to the IC ground are essential. You could also consider adding reverse biased (negative clamping) diodes on these pins (to prevent them from somehow going below GND). A negative clamp diode at the SW node can be helpful too.