You more or less eliminated my troubleshooting list. . . . lol
If you can run onboard Graphics without issue, I would think that you have an issue with either the PCI socket, where the socket attaches to the MB or somewhere downstream on the MB itself.
I don't think I am saying anything you don't already know, but if you are creating demand on the GPU when it crashes - it sounds like something is heating up disrupting flow. If it isn't the PCI socket, then it has to be the MB. The outlier would be two bad GPU's - while probable - its unlikely.