Could also install a ssd, no spinning disc means less heat, then remove the psu and mod a pc psu and use that, again less heat.
Slims dont ylod as much, if ever if treated right. Reballing while it's still working sounds overkill and probably would ruin more than it fixes. Never touch a running system
The same best thermal paste which is used for PC CPUs. I think it was Arctic Silver 2
Arctic MX-2 is a hell of a lot better.
I wouldn't touch that conductive rubbish even if I got paid for it.
Replacing the paste from underneath the IHS is tricky and you can kill your RSX and CPU really quickly if you're not careful.
Replacing the paste on top is incredibly easy.
Do note that your heatsinks could be stuck to the RSX/CPU.
I wish they had copper replacements for the heatsinks in all honesty ;/
As for the reason, silver is conductive.
It shouldn't pose an issue but smearing conductive paste onto electronics should be a no brainer.