Since it's so intermittent, sounds like the door lock power is getting stuck on and keeping the lock energized for long periods of time. Otherwise in order to do that much heat damage in a short period of time the lock would need to see very high current for a short period of time...which is unlikely assuming the door lock power is fused or uses a PTC device for overcurrent mitigation.
On the really weird side, we would always switch the (+) leg on a DC lock since many power supplies have the negative rail at ground (more or less). I have occasionally seen strange things like this happen if you are keeping the (+) always on and switching the (-) side. If the lock wiring or sometimes the case on a metal door shorted to ground, it could keep the lock energized.
Here is what I would try:
1.) Measure the current for the lock and make sure it is within the manufacturer's stated specs. Since you stated that the power supply is 12 VDC, 5 A, and I'm guessing the lock current is less than 500 ma, if the 2 REX normal press switch for that door is getting stuck in the on position it could definitely cause this.
2.) Make sure the power leg for that lock has a suitable fuse in line from the 12 VDC, 5 A power supply. If so and the lock still burns up, most likely cause is voltage sustained longer than just a few seconds at a time. Sometimes this can also be determined if the lock handle is warm to the touch.
3.) Check with the Allegion/Cisa to see if they have a bad batch of lock solenoids, etc. Have seen this happen with Schlage in years past.
Please let us know what you find out in the end. Good luck!