How about a composite unicycle? If some of the major components of the
unicycle such as the frame or seatpost were made of fiberglass (or carbon
fiber) you might be able to achieve a significant weight reduction. This
might make up for some extra weight in the drivetrain.
Also, perhaps a small unicycle, say with a one foot shaft, as a proof of
concept model. If it worked well you could then go on to bigger and better
unicycles...
Alec