So here's what I think I'd need:
-3-speed lawnmower transmission: $20 + $11.54 S&H from Surplus Center
-7 tooth #41 sprocket with 3/8" or 10mm bore (think I can bore out a 3/8" sprocket to 10mm?) for the input side of the transmission: $6.41 from McMaster-Carr
I'm considering experimenting with one of these too.
I think you may need a much larger sprocket on the input side of the tranny and a smaller one on the engine.
If you can add a pillow or flange bearing to the output shaft, outboard of the drive sprocket, the stress on the axle bushing would be greatly reduced
What about a clutch? This tranny's clutch, I think, is just in or out, no friction to soften engagement.
I would use a v-belt primary drive with a manualy controled idler for a clutch. Easy to change ratios too. A cent. clutch would work also but may require different method of shifting on the fly.