I figured out a way it could work. It is a bit tedious... but it may work. Start up the game with the map pack, THEN sign out of that account and go onto the one you want to play with.
This worked with an arcade game of mine. I couldn't play the full version on one GT but on another I could. So I started it with the one that could, signed out and signed onto my normal GT which doesn't have it.
And you CAN get Gamerpoints or whatever their called from this too... Hope this helps someone!