The first, and most obvious thing to me would be to pull everything ahead of the amp out of the system and use a phone, or other standard audio source. A cable box would be good as well, with standard RCA connections on it, or in the case of a phone, a 1/8" stereo to RCA cable and plug that into the amp instead of the turntable/preamp setup you have. This is cheap and gives you a source which will be free of over driving issues.
You want to leave the amp on variable, it should not be in bridge mode, input sense should be off, speakers should be on the 'A' terminals exclusively.
I would recommend disconnecting one of the speakers during testing. Test one speaker only, then if there are no issues, move that speaker to the other terminals. If that speaker continues to work fine, disconnect it, then connect the other speaker. Test that speaker on both terminals (left and right) just as you did with the first speaker.
Now hook up both speakers in stereo and see how things go.
This will help to determine if the amp is the issue, the speakers are the issue, or if you have an issue ahead of everything that is causing the problem. A bad cable can certainly present an issue and I've seen my share of bad RCA cables over the years from major manufacturers. Speaker cable almost NEVER is an issue. Running speaker cable wrapped around power cables wouldn't cause this type of issue. Let alone separating them as you have.
I've seen dozens of amplifier channels fail over the years. I'm pretty sure NAD was one of the biggest culprits to this issue.
Anyway, this isn't something I would diagnose using equipment that may be faulty as well. Start with known good product, and insert into the system to test it out across the board.
