A major solution to this issue is covered over in
this thread, for anyone with a similar problem in the future.
The TL;DR version is, you need MobiMetaEditor, which you can find
here.
MUCH THANKS TO shamanNS!
HOWEVER: I still have a handful of books without covers. Calibre says they have UUIDs, but MobiMetaEditor says they don't. Several books even have book covers in \system\thumbnails, but for some reason my kindle doesn't register their existence.
Help???