Mac Pro 2.1 (Eight Core) sudden restart

So I bought this mac (pretty cheap) knowing it had the problem.

Basically, the machine will run for a few minutes and restart without notice. It'll eventually restart sooner than the previous time and so on... it'll even restart itself during the power-on chime.

I have had the "CPU A & B OVERHEAT" leds turn on on the logic board, but it's not always the case.

What I've come up with so far:

-Not a bad RAM issue. I have changed all FBDIMM sticks and swapped risers.

-Not the graphic card. I run the machine without it using screen sharing and it still restarts.

-Not the battery, I put a brand new one in.

-Multiple resets of SMC and PRAM

I have managed to install Hardware Monitor on it and I have witnessed several current and power peaks on idle:

The machine crashed a few minutes after this grab.

Are those peaks and oscillations normal? If not, does it qualify for a faulty PSU diagnostic?

Also, I have noticed that the fans always seem to be running at the same speed... I got control of fans speed by installing smcFanControl but does it point to a more specific trouble?

Also, running fans full speed seem to let the machine run a little longer.

If it's a bad logic board, I'll probably have to give up on it.

My project is to troubleshoot it myself so please, don't bother suggest I should bring it to a tech or get a newer machine 😉

Thank you!