I had a similar issue a month ago, went the new PS route and like you, problem continued. I took out vid card and memory then gave them a quick sanding with 2000 grit paper then an alcohol wipe and reinserted. Then removed every SATA connector on MB and drive and gave all a light spray with INOX and restarted, problem gone. As a LOL I did not properly restrain a PS cable and it wound up eventually blocking the fan on my AIO, the CPU then went to 98C and promptly BSOD'd. I think you've found your problem by moving it out of the case and running it going breadboard, now find a good cleaner/lubricant and do a through contact cleansing while it's out of the case and easy to do. I like the INOX because it's not greasy like WD-40. I think all of us are guilty of forgetting just how many connections are involved with a modern machine and the consequences of just one of them not functioning properly, best of luck and welcome to AT, while not as big as it used to be, still balls-deep in nerdpower!Vcore testing and under/over clocking made no difference, crashes happened both at 1.6Ghz and at 3.8 turbo, as well as lower/higher voltages. I am breadboarding for 2 days in a row without crash now. I will use this for a little bit longer, and report the result. I am actually very surprised this might have been a problem with the case :O. I'll let it go for few more days just to be sure, and let you guys know.
By the way thank you very much for many of your suggestions here, I am sure many of them could as well helped either me, or people with similar issue who might read this post.