Thanks again. It really helped to realize I need to restart MusicBee to have it refresh. I couldn't understand when/why it was updating.
It also isn't an issue of mixed album tags, it affects track title tags too. I think I've figured out a bit more of what's going on, but it's almost worse than I thought.
It seems like MusicBee only stores/calculates one automatic sort tag per case insensitive track name. This means that if two different artists/albums use that track title with different case, one of them is going to get the wrong sort title case.
I added an image of my experimenting. Unless I'm missing something, this is the reason that my sort tags keep changing. Any time I re-use a track/album title elsewhere in my library, it affects completely unrelated track/album tags, which due to my organization rules, renames files. Plex hates file names changing case so it's really a problem for me.
Columns: artist, title, sort title, album
Ugh. That's not the whole explanation. I switched the manually added sort title for AYA back to PRISONER and restarted, and this time it left the other tracks alone. I don't understand what's going on.