Assuming the power and amp remote wires aren't shorted anywhere along their length

Even if they were, they wouldn't blow the fuses in the amp. The fault has to be after the fuses (i.e. in the amp).

Unplugging all but power is good idea. It would seem you have some sort of short in the amp. If you're sure it's out of warranty, see if you can pop it open and look for anything obviously dodgy inside. It could be as simple as broken power wire coming loose and contacting the case which is likely to be grounded.