I was thinking this application using a 3-speed coaster brake hub, not a multi-gear derailleurGood idea in theory but there is a 1.7 to 1 reduction on the left side currently so running the gear box output shaft directly to the right side will eliminate this added reduction which would require you to run about a 70 tooth sprocket on your chainring. I don't think we have enough ground clearance for that.
set-up, then maybe run a 52t front chainring (rather than a 70t) and a 22t on the rear. Or something like that.....