Not having much luck with this. First, Picard seemed to struggle to identify much of my library, which is rather messy and consists of tracks from a variety of sources rather than necessarily full albums. And then even for the tracks it could identify, clicking "Save" on them didn't seem to actually do anything to the files/tags as far as I could tell. Maybe I was doing something wrong.
MP3Tag does seem to effectively modify the files in the way I want (except that movement numbers aren't displayed as Roman numerals, but that's pretty minor). But I'm having a hell of a time getting these changes to actually "take" in MusicBee itself. When I look at the track title field in MusicBee, it still shows the old value, even though in Windows Explorer the new title is shown. Is there a way to get MusicBee to take notice of the updated fields somehow? Sorry if this is obvious, I'm not good at this stuff.