Like you wrote an electrical problem "wouldn't explain why it's getting so hot so quickly".

It could be one of those strange faults like a loose exhaust baffle blocking the silencer or a cam lobe "gone soft." Seems like it is going to be difficult to diagnose.

Well, I think we figured out why it intermittently ran really well when hitting a bump and working rough the rest of the time. My nephew moved and lost the key so he had to hotwire it to drive it today and it started on the first pull and is running great. He said it feels like it's still running hot though, but it starts right up even when it is hot. It's running a DR7ES right now, I wonder if a cooler plug like a DR9ES might help it run cooler?