How do I "use a multimeter to check if one of the AC runs is miswired"? And how do I "orient" a two-prong plug? How do I diagnose, and what do I do about, an "open AC neutral run"?
Set the multimeter to read ac volts, on a scale that is greater than 120V, such as the scale that many multimeters have that reads 0 to 300VAC. Then for each outlet measure the voltage between hot and neutral, hot and safety ground, and safety ground and neutral.
How to orient a two-prong plug, if any, I explained in my earlier post. I'm referring to the fact that if the two prongs are not polarized (i.e., one is not wider than the other), they can be plugged in with two possible orientations.
If an ac neutral run is open, it should become apparent by performing the multimeter measurements described immediately above (i.e., you will not see any voltage between hot and neutral).
If you don't have a multimeter, or other ac voltmeter, or you don't feel comfortable doing these things, try my other suggestions first and if they don't lead anywhere perhaps you know someone nearby who has experience making electrical measurements.
One more possibility occurs to me: Somehow either a large dc offset or an ultrasonic oscillation may be being sent into the speakers (both would be inaudible), causing speaker driver or crossover elements to heat up excessively, producing the audible symptoms after the 20 minute period. Not sure what might cause that, given that you've apparently tried multiple amplifiers, and I'm not sure how a dc offset would affect the midrange-tweeter part of the spectrum, but I thought I'd mention these possibilities in case they trigger some further thoughts.
Regards,
-- Al