I have now done enough testing to conclude that the Intel 5520 chip/set was overheating, similar to this forum post I found. I had a hunch it'd be something to do with the chipset so I did a bit of searching, and this scenario was very similar.
This toasty boy right here.
This was the testing solution while doing troubleshooting outside of the case a couple of days ago, all crashing stopped from this point onwards.
And finally the permanent solution. I cable tied this fan to the screwholes unused by my ATX Define R4. Haven't had a crash so far.
Fun fact, the fan came from a computer I got for free from the dump. It's actually a really strong fan and it's really quiet too.