That did the trick for some of the files. The Tag Inspector wasn't showing any APEv2 tags, and only the IDE3v1 Artist, Album, Comment, Genre, Title and Year tags, so I wasn't expecting removing the tags to work. Tried it anyway - removed all Replaygain tags, recalculated them using dbPowerAmp, and now they are recognised by MusicBee!
Still had a stubborn album that refused to play along with this process - in the end I got MusicBee to do the Replaygain analysis, which worked fine. Subsequently redid it with dbPowerAmp (for consistency with the rest of my library), and the tags are still recognised - so no clue as to what the issue was there.
Hadn't seen the Tagging Tools before, so thanks for pointing it out!