Just an idea from something I've seen, with a new thought. There's a similr problem when trying to do tank treads, or chain drive systems.

Though, they differ in that it's lots of little pieces, rather than a single belt.

What I'd try, would be to create the belt and then an IK chain - you know, heaps of bones. This would give you the flexibility to move around corners, but still no movement. From there, I'd see if I could attach the joints to the curve you've drawn and see if you can get them to run around it. If so then the belt should follow and even flex in al the right spots.

Then you'd just have to chuck some writing on the belt, to rotate as it did and voila! One moving belt.

S.