Wow, I can't believe that I never thought of that! Of course I don't have to attach the sprocket to the axle if the mechanism itself is attached to the sprocket!
Now I just need to find a shaft material that can take the weight (or some way of taking the weight mostly off of the shaft), which will probably be quite high (since the chain on the back side of the 3.5825" radius sprocket will have to exert about 600 lbs. of force
to balance the weight at the end of the lever on the other side - we should probably look into doubling up that 60-tooth sprocket and using double-strand chain, since 600 lbs. is almost twice as high as the working load that I recall seeing for ANSI #35 chain, but it should be doable at least). According to the IFI spec sheet, the sprocket can accept a .5" bearing, and if the shaft is really well-supported that should be possible (since there won't be any torque exerted on the shaft itself).
I guess I still need to work out how whether the middle shaft (with the 48-tooth and 9-tooth sprockets) can be attached to said sprockets or whether it will be necessary to somehow rig them together on a dead axle as well, but that seems to be a somewhat easier problem to overcome.