Surely a timing belt for the outer gear would have the wrong profile.
i compleatly missed that,,, i think your right

iv got another one for you to ponder... there is probably somthing obvious iv missed but if you use a double sided timing belt you might be able to exit the belt through the outer gear wall (using small rollers maybe) to drive an output pulley, that
might solve the main stumbling block to the idea and give you a sturdy output (if it could be made to work)

Click image for larger version.  Name: T%20Type(Double)%20Belt.jpg  Views: 635  Size: 28.8 KB  ID: 3486

it would make an interesting project but i think im going to admit defeat and try to get a second hand hi-tec drive :)