Hey guys, to address your thoughts:
-I don't lose my save files with the system off. I actually just tested it now, and the save files I made on 11/30 are still there. I haven't used it since then.
-The memory's not full...I've formatted it several times.
-I don't think the SSC 3.0 is at fault; the save issues and graphical screw-ups still happen with the regular System Card 2.0 and the Arcade Card Pro.
Another thing I wanted to try is a CD game with automatic saving after each level (like Valis III). As I expected, the game loads OK, then all the cut scenes play, but the game locks up before the last cut scene that precedes the first playable level.
Hopefully when I finally have time to open the dock and poke around something obvious will pop out, but probably not. I'll start with replacing the supercap (which I would give only a 10-15% chance of fixing the problem) since it's a cheap and easy solution. But not until after the holidays...I'm swamped!
Thanks again for all your suggestions, thoughts and perspectives. I welcome them. If this is "a thing", then I'm probably not the only one who's had or will have this problem. It would be nice to have some data about it.