In Windows, they call this the Blue Screen of Death (BSOD). That's basically what the MCE is. Your system has a hardware problem. Have you tried clearing the CPU fan/heatsink of dust? It could be caused by poor cooling. Maybe open the case and point a fan in there? It sounds like you're on the right track of elimination. If you're positive your PSU and RAM are good and you've disconnected non-essentials, then I'd start suspecting the CPU or main board. Does the system fail at this point every boot?
I believe MCE errors that are correctable are written to /var/log/mcelog; otherwise the system halts and reboots. With Unraid, that log is probably empty regardless because the OS runs in RAM and logs aren't retained between reboots.