internet troubleshooting is never easy and it seems like you've been through this pretty thoroughly. that said it really sounds like the pump is losing prime. i would think even with the relief stuck open some it would still push some oil out the pressure port. oiling systems aren't very complicated so unless it's some bizarre problem it has to be something you've already looked at. i would concentrate on the suction side of the pump and that's a pretty straightforward setup. being it sounds like such a weird problem maybe using a drill and priming drive might be worth a shot to see if you can duplicate the problem without running/cycling the engine.