There does appear to be an unexpected incompatibility with Music Menu - in addition to the one I expected (playing a track through my plugin does not add it to the Music Menu), it seems like trying to play a track presently loaded via LoadBGM through the menu does not work (no errors, just nothing is played.)
I can't imagine why there would be an incompatibility with any other Yanfly plugin, and that one might be fixable.
EDIT: And now it's compatible with Music Menu. (You should put this below that in your plugin list.) If you have any issues, let me know!