I tried a Teamforce SSD and Fatxplorer didn't have it, but funnily the PNY SSD I had set up for my PS3 ended up with the right flash chip. I just cloned from the PNY to the Teamforce, and the PNY got set up for the Xbox 360.
Both consoles run smooth as butter after that.

At any point, have you considered swapping to SSDs? It won't solve the inherent risks of the old dogs but it made both of them fly through dashboards and loading screens.
PS3 is easy enough, 360 requires a licensed app called Fatxplorer and the SSD needs a compatible flash chip, but it's worth it.

Not a thermal paste issue - cheap low-tolerance solder that melts at the temperatures the Cell and PowerPC chips reach. It's unfortunate, these machines need full reworks with properly high-quality stuff but they're seemingly plentiful so people just chuck em without remorse.

This sure is a statement. It has no nuance or substance, and it doesn't address a single matter here, even a vague hint that "we are continuing to diagnose the problem" just "We hear you. Thanks!"