I'm a pro right?
Sounds like your amps... The power supplies have a habit of either earthing out when they get older (tiny bits of metal here or there, I've seen Alpine miss a shard 4 times that f**ked up an expensive amp), causing them to flow power all wrong and heating up like a light bulb...
But in the same way, the amps can f**k up and send off a largely f**ked power signal (dealt with that myself, there is a technical term for what happens, but I had a big one last night, gimme a break ). Either way, I have come to find that the sompanies that make the hardware, are not all that interested in helping you out... they would rather you just buy something new... That being the case, run all the normal tests, move amps to other cars, try different wiring, though it sounds like you have tried half of that stuff...
Another thing I would suggest is to take it to a proffesional amp fixer who has nothing to do with the company, some people outsource their amp fixing to some really shitty companies (never EVER break an earthquake amp, just trust me on this one...) and they can VERY OFTEN miss something, and not fix it...
Good luck though, sounds like a rather unique problem
Edit: For the record, I may have had the same problem once... My amp got extremely hot (never on fire, cause I was testing it at the time) while just being on... never cranked, never put under and decent sort of load for a 3000WRMS amp... The mosfet power converter was farked... i think... again... big night...