I am not an expert, but I know some people here are, so do defer to their judgement. But, I'll give you my thoughts:
I don't think this is an issue with the processor being generally unstable, and I am certain that more vcore is not going to help. My best guess is something to do with the RAM. I saw that you ran Prime95, which is great. It only tests 1600 MB of RAM though by default. Go ahead and lower your vcore back to normal, and DRAM voltage to whatever the stock value is for your ram, probably 1.5 V. Open up Prime95, set it to custom, and put in something like 10000 MB for ram so that it has to test all three sticks, and see what happens (I'm going to try that out on my system in a minute to make sure that is ok lol). I am thinking that you will see a crash, since it crashed when loading up many virtual machines.
Another test to try if this doesn't show anything useful is memtest86
I hope that is helpful; this really is an odd problem to be having.
Edit: Yep, set Prime95 to 10000 MB of ram, that gets about 11 GB loaded up for me. Also, apparently you can get a more thorough test in less hours by setting the time thing to 5 or 10 minutes rather than the default 15.