Yes, but............

I wonder, is the overheating due to the door circuit or the rear speakers?

Remember, the feed to the rear speakers is separate from the feed to the door speakers.
If he has not changed the rear speakers, then go for it, the problem would be in the door speakers. But if he has changed the REAR speakers, now the overload can be the door circuit OR the rear speakers.

That is my only 'caveat' here. It SOUNDS like he's only changed the door speakers, so separating them would, it seems, solve the problem.

I'll tell you one thing: I am rather impressed by the protection circuits of the factory amp.