I'd try one more thing I think. I'd see if it cuts out with the volume all the way down. Then, if it does, I'd disconnect the inputs from the amp & see if it still gets hot. One possibility might be the preamp is dumping a high freq oscillation (>20KHz) and that is heating the amp up. It sounds like it really is thermally shutting down. I believe each channel is thermally protected seperately. It would make sense the two outermost physically channels in the amp chassis would be the coolest & least like to shut off. The transformers are about the only shared component in the amp, so its pretty odd that all channels are shutting off. Could your line AC voltage be really high?

One more thing you could try if you have some extra wire. Run the wires to the speakers with the extra instead of the in wall. Maybe some weird load caused by the wires is causing the amp to go unstable & oscillate at a high freq, which would make it get hot.
good luck