Sounds like you may need to remove the Daughtboard and reflow solder on the connections between the Eprom socket and the daughter board.

The Genesis I am currently restoring was a no-op when I first bought it, it would do really really strange stuff. I went though all the grounds, cleaned connectors, checked caps, etc. Then I finally broke down and removed the daughter board and sure enough the solder joints were cold and making intermittent connection. Reflowed the solder on board and it has been solid since then

I had to use a magnifier to see the small cracks in the joints on the Genesis I redid.

Yes definitely remove the old solder.

Make sure you are using a good flux core solder too.