You could experiment with several things. Here are a couple untested suggestions.
Shift to an identical room with the shift set to stop music. This new room would have no music and a shift on touch in the same spot to a third identical room that starts the music over.
Set two bank musics to an identical track (for example, track 1 = track 2)
Shift from a room with track 1 to an identical room with track 2.
Use ambiance with a very large gap of silence at the end of the track and then a normal music bank.
Shift from a room with ambi 1 (the audio) and music 0 to a room with ambi 0 and music 1
This method would have a much more abrupt stop than the other two.
You would then experiment with different shift shapes and place those in the places that would kill you.
I'll test these later