You may have already considered it, but ram makes an attachment point that you can just replace an existing screw/bolt with the ram ball.
I don't know how it would hang on the visor base but I used this on the bottom right of my dash bezel. (fj60 solutions switch plate in place of sandwich...
Dang it! I bought the ashtray replacement a couple weeks ago but I think the sandwich tray replacement would be better. I just bought the new one so if anyone wants my ashtray replacement DM me. I'll make you a good price.