Update: it really does appear that the BSODs only happen when CPU is idle. So far it seems that as long as I keep the clock up under windows, no BSODs will happen.

I tried installing windows to an USB stick to see if a clean install might help. The USB installation could not even finish due to BSODs, although this could theoretically be caused by the fact that it was running off a USB stick.

I have ordered some Hydronaut paste, I will try re-seating the CPU once it arrived. Maybe some dust got into the socket during replacement and is causing problems if the voltage goes too low?

Bumping SOC voltage was recommended by some, does it void warranty?