Great, I hope we can say finally this puzzle is solved!
It looked and smelt like an EPROM problem all along, what threw us was when you reverted back to the factory PROMs and there was still a failure.
Some programmers (I don't know about the GQ 4x4) will also verify at +/- 0.25v on the 5v supply to check if the write was good.
I have a Chinese TL-866 EPROM programmer. It programs 2716 EPROMs and always verifies the write as good. I put those EPROMs into a MPU board and they always fail checksum. If I verify those 2716 EPROMs in a professional programmer, the verification also fails. When I rewrite the 2716 multiple times in my TL-866 then they work properly. So I've seen this before with EPROMs not getting a deep enough charge that makes the data susceptible at certain supply voltages. Infact it was the very first thing I suggested at the start of this thread
Anyhow it was good to see you didn't give up and weren't intimidated with your oscilloscope, we learnt a few things.