Why dont you just compute the torque needed as suggested? You should find that it does not depend on the moment arm. However, since the torque is constant, you need to supply less force on the chain with a longer moment arm.
Is this correct? From what I understand the torque the chain applies on the wheel must equal the torque from static friction if the bicycle is traveling at constant velocity. Based on that I am able to determine the output force from the bicycle wheel.
But what about when the bicycle is trying to accelerate, is it friction or the chain that supplies the net force and net torque on the wheel? If friction is what supplies the net force, then wouldn't the bicycle roll backwards(friction would give a ccw torque)?
And what exactly happens when the bicycle slips down the hill? If you are in a small gear, then you have small output force which means you get less static friction. So then is it that because you get less static friction, gravity's x-component supplies a net force causing a downward acceleration?