Ok, so I worked through all the files with missing/duplicated tags in TagScanner on my desktop and re-copied them over. The number appearing under "Unknown album" by "Unknown artist" has dropped to 41 tracks and "Unknown genre" has dropped from around 140 tracks to 94. Some files that only had 1 or 2 missing tags (ie. some were missing "Album Artist") have now lost even more tags.
Things are still a mess, basically. And I guess TagScanner won't let me check the tags on my phone directly, but copying files back again over to my PC showed the tags were all still intact, so they should probably be copying over with no issue.
The example album I've been using, Boxer, seemed kinda fixed... for a long while the TRACK TITLES were all empty though, even after Rescan/Full Rescan and an uninstall & reinstall. But I booted the app back up when I woke up, and with its initial scan it seemed to fix that issue itself. So, I guess that's one album totally fixed somehow. (You can also see the other issue I'm having with Poweramp in the screenshot though - the wrong track appearing as now playing on the bottom. It seems to take the tags from the track with the corresponding position in the general "All songs" list.)
The album with the file 6b6561 checked out, Iron Front, is no longer missing artist/album tags... but is now split into two albums for some reason.
Funny enough I came across this exact topic while trying to troubleshoot, but I couldn't see any .cue files (with Show Hidden Items checked in Explorer)