You probably remember the old Peerless F-N-R riding mower transmissions. Big pulley on bottom for vertical shaft engine and a tiny sprocket on the side. We never got a sprocket off, but we did put some pretty small pulleys on them. I found a three speed one and put it on a Boonie Bike frame with a big cast iron Briggs vertical riding mower engine. I remember having a Hell of a time getting that 1 inch PTO hole in the engine plate.
We rode that bike for a couple of years, never changed the belt. Sometimes we had 3 kids on it, going across muddy, plowed fields to get to the woods where we had trails. Yeah, the belt got muddy, wet, slipped and came off a lot, but we loved it.