I tested this on my setup. I’m using a 32x on a CDX, and an everdrive. I got the same dropouts during the crusader of centy opening screens up to the point where you make your character, like 2 or 3 sync drops as it transitions between the different screens. I could not reproduce any drops once in game while going to the save screen though.
I’ve previously played through Phantasy Star IV without any problems the entire game with the exact same setup/settings, so seems to be something caused by the specific game. You mention some other games, do you have a list that you observed this problem with?
Edit: From what I can tell this is not due to a resolution change, says 262p on my ossc screen the entire time.