Paddlewheels are more efficient than props when the speed is low and the resistance is high. For instance, for large river barge tows. But once you get outside of that comfort zone the only reason to use a wheel is for its low draft (about the same as the hull itself) or because you just want a paddlewheel!
The major difficulty with wheels on small boats is two-fold. First the larger the wheel diameter the more efficient it is, but a small boat limits your wheel diameter. The classical way of dealing with this is to use feathering wheels. They mimic the motion of a much larger wheel. Typically, they are used for side wheelers, but I mocked up and ran a jon boat with a feathering stern wheel.
Secondly is that wheels are surface drives and the depth of their floats (paddles) is critical. In a small boat the wheel's depth is changing as people move about the boat.
For a large speed reduction I'd look at SS chain or cogged belts. My fave belt is the Goodyear Eagle herringbone belt drive. Very efficient, quiet, and self centering.
Hope this helps.
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