It might be worth trying to run it through trickle to limit the allowed upload bandwidth.

http://monkey.org/~marius/pages/?page=trickle

[Edit] I see someone else has linked to trickle above.

I didn't see it uploading a lot over about 20 minutes. (1) I was listening to an obscure album, (2) I listen to small number of songs repeatedly, although I have a large number "starred" and in playlists from previous installs of the app.