The method you are using has been used from the beginning, all the early motorcycles were using the sprocket in the cranks to transfer the power to the rear wheel. look at a 1903 Indian, its not new. A two speed gear box is all you would need, a bicycle should never be over 30mph for long, keep it safe. Have fun, Dave
This is a pic of a stock Honda 50 gearbox, only 2.5" wide. Three speeds.

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Chuck - The monkey has the spark plug again!