drain pan overflow safety and blower door are the most solid answers so far.
high head wouldnt cut the tstat out, the air handler and condensing unit are on separate circuits(well, i hope they are), and the high head would kill the compressor only and maybe the CFM as well depending how its wired.
alot of the times as well, if theres a circuit board supplying your 24v and controlling the air handler, that could be causing issues, but i find it highly unlikly because if that was the case, it would not have intermittent issues. it would just fail and not work. 9 out of 10 times.
transformers 99.99% of the time do not fail intermittently, its either working or not. but electrical can act fucky at times. so dont rule that out just yet, put it last on your list.
intermittent issues like this are usually caused from a safety switch (door switch, overflow switch) or a loose wire wiggling due to a vibration.
goodluck, check the dumb stuff first, if you cant figure it out, call a tech. you dont want to blow up boards or fuck anything up. tape the door switch as if the door is closed, and see if that fixes it, look at the drain line, check thermostat wiring in the airhandler for snug/tight connections (hit the service switch before you poke around)
another stupid thing to check is to see if the breaker in the panel for the air handler became loose, wiggle it around and push it in tighter, ive seen that a few times.