I did not read all of this thread:
But to answer your question about what usually causes the motor to lock up and flame out on a electric air compressor is the piston head on the compressor does not unload the pressure off the piston so as the motor can get a running start at a unloaded piston.
You should hear a pist (air spew) immediately when the compressor shuts off when the cutoff pressure switch operates.
If you can bleed off the air pressure from 100 psi to around 25 and it starts ok this tells you it's most likely not unloading.
If you hear air constantly leaking when it shuts off it's the air supply main check valve leaking back to the compressor.
Some cheapo unit use what is called a genie valve, it's a combo check and unloader and it's common for those to fail.
If you do not hear this one time air spew WHEN THE COMPRESSPR RUNS IT'S COMPLETE CYCLE) your UNLOADER is not operating which is usually built into the pressure switch on the small air compressors. You can research such on-line.
Now keep in mind if the compressor is running and gets' up to a pressure of say 80 lbs and it normally cuts off at a higher pressure and you unplug it or it losing incoming voltage the compressor won't unload from the pressure switch unload because it did not complete it's cycle. A genie valve will unload because it sense no air flow and the larger industrial compressors sense when to unload by using a centrifugal unloader built into the compressor PUMP. (anytime the PUMP is not rotating it's in the unload state) This mechanically protects the driver motor from a lock-up seizure.
Summary: Most likely your unloader. Research such online and watch you tube video and read your owners manual.