Another re-read later . . .
You've only had problems with two channels at a time, though one channel appeared to change. This problem has only been with the hardwired mics - the wireless mics simply didn't work in the show.
I wouldn't rule out problems with the amps or power, but this is a long shot. Were you bi-amping? This kind of problem can occur when the bottom half of a biamped pair goes down. If your amp wasn't happy this could be the result.
I think it's likely to be cable. The reason that problems were only with speaker 1 and then subsequently only with speaker 2 may be that you switched cables when changing from the lavs to the ATs i.e. cable 1 plugged into lav 1 (and c2 to l2), and you chaged to cable 1 to AT2 (and c2 to LT1). Does this sound possible? You don't mention whether the audience mic was ever working correctly (you say you didn't have time to test it).
If your setup worked flawlessly with the wireless mics then I can't see that they are the issue - or the amp, mixer, speakers and speaker cable. When they didn't work, they simply didn't work. Your mics worked when wired in without the snake (as did the rest of the system). Long cables (200m) aren't a problem - bad cables are.
I'd put my dollars on it being a cable issue.