Well guys, I'm a little embarrassed, but I think I can say "false alarm" about this one.
Formatting my memory fixed the problem. This was something I was hesitant to do before because I had just achieved 100% in Dracula X for GOTW. However, tonight, I said to hell with it and wiped it out, and that did it. My disc works now.
You know, back when I got my first Duo, I had a problem slightly similar to this. I had a Tengai Makyo II save that corrupted, and the game gave me an error message when I tried to load it. A couple other things in the memory got screwed up a little bit as well, and it was just generally acting weird until I did a format. Once I did, though, it didn't give me any more trouble.
Here's hoping this does the same? I don't know...I'm a little scared to save anything important to it, at least for now. But it could be that not being turned on for ages caused the super-capacitor to get so low that it caused trouble. I might try leaving the system on overnight to give it a good charge.
Thanks a million to everyone who checked their disc for me, and especially to the guys who took the trouble to rip their copies for me. I really appreciate it.