I will go the opposite way of “the most common fixes” assuming you’ve tried them, and suggest a couple of random things you may not have thought of: First I’d check the GPU’s PCI-E slot, and clean it with a blower/compressed air on both ends and reseat it. GPU could also be sagging down as i assume it’s a high end one. If that’s the case, see if you can prop it up with something on the corner. You could also try another slot for it if you have one on the motherboard as a alternative solution - I’ve had a GPU slot go bad before, and switching to the second slot helped.
That reminds me, double check if the PSU to GPU power cords are plugged in, and assuming it has multiple plugs don’t use a Y-splitter but use separate power cables from the PSU to the GPU.
My second unlikely suggestion is based on a similar problem I had many years ago and the cause turned out to be a grounding issue caused by a powered USB hub. I’d test the PC with every externally powered device unplugged (except the monitor I guess) and see if the issue persists.
It could also be a good idea to confirm that the Displayport works without issue as I assume your relatively limited time with the VR headset could be misleading given the nature of the issue - maybe try to get hold of a DP to HDMI cable and hook the monitor up there?
On the other hand, I also wouldn’t dismiss the monitor just because it works with other sources. You’re most probably right based on your experiences but trying the PC with another display -could use a TV if feasible- until you get the problem again would narrow it down to the PC definitively.
Anyways, I hope my suggestions help cause this kind of intermittent problem is really difficult to troubleshoot and very frustrating, so I wish you good luck.