I tested three ideas and all of them work.
The first is quite similar to the one you described, the second involves two music tracks and the third is the same as the second but using ambiance. The track is Blah in Progress by Nifflas.
They all sound quite different and have their own advantages/disadvantages.
This is a small example level that demonstrates all three :)
http://www.sendspace.com/file/klxkco
Jump into the spikes, pretty straight forward.
There is a blue/yellow tile indicator at the top of the screen to tell you whether you're in step 1 or step 2 of the music shut off.
Use the level editor to learn each technique if necessary.
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 :)
Happy knytting :)
~Dj