Amphibious Bike Propulsion Problem!
If you want to drive from the chain (a better engineering approach), why not have a sprocket on the other side of the back wheel? I once had a bike with a fixed wheel sprocket on that side so you could use the wheel either way round. To engage / disengage, you could have a dog clutch as part of the right angle drive system. That bit would involve some serious metalwork, though.
Would an electric distribution system be out of the question? They do it in many high powered vehicles. It would solve the angle and control problems - but then there's the water to consider!