just some ideas
have you tried testing your ram? (mem86 or such)
how long do you game before it reboots?
have you checked your cpu and gpu temps at idle? under load if you can game for 2 or 3 min before it crashes?
computer resetting when loading games can be more then just the graphic card
I would say you eliminated the psu as your issue after trying three different ones so time to do other checks