I'm sorry but a gear drive shaft setup will not come close to a chain drive in efficiency related to power transfer. the typical 90 degree gear type setups are around 85% efficient and you won't find them on a bike. Consider you will end up with two 90 degree gear setups, crank to drive shaft and drive shaft to hub. And you might as well count on 20-25% power loss.

Trust me. If this were such a great idea and superior to chain drive systems it would be the mainstay for bikes worldwide and Lance and his buddies would be riding them in the tour.