Just to make sure I understood that part correctly, does the linux install crash while running live too?
You seem to have tried most of the logical procedures, I could only think of doing a bios update in case this was some sort of weird bug with your specific hardware combination. If that doesn't work, then the only thing left would be to try another PSU. But as you said, it doesn't sound likely to me.
Yeah, running the Linux distro live crashed with the Linux equivalent of a BSOD. I updated the bios the first time I saw a bsod, and I doubt there have been any changes in the last month. I'm going to run some test on the SSD next. However, I have no idea how to debug between the CPU and motherboard so if its not the SSD or PSU i'll definatly be stuck.