And now the good news . . .
I uninstalled iTunes 11, installed iTunes 10, and had to let it resync my iPod 3 times (no idea why it took 3 times), but it seems that now everything is okay. I haven't checked the iPod, but at least the iTunes music library plays my musical gapless. I didn't have to buy a bunch of micro SD card, or a $1,300 studio-quality player (which looks REALLY nice and I REALLY want, but can't afford). All it took was uninstalling iTunes 11 -- plus some registry edits, and searching for and removing some files Apple installed deep in the OS -- finding, virus scanning and installing iTunes 10, and 48 hours to re-scan my ripped CDs into the iTunes music library, re-download the album covers, and resync the iPod.
And people wonder why, when they tell me they have a Mac, I ask why they didn't get a real computer.