Have been away from the forum for several weeks (surgery), and now have a lifting limit of only 8 pounds for several more weeks. I have almost never seen such a large amount of discussion about how impossible and impractical it is to build what Jeff F. wants, although in my mind it is not such a daunting task as many of the "nay sayers" indicate.
Building a small plywood hull sternwheeler is no big challenge, has been done many times.
As to paddlewheel propulsion, it works OK, although not as efficient as modern propellers. What Jeff F. wants would be a boat of about 1 ton displacement, 16-20 ft long x 7-8 ft beam, with independent electric driven stern paddlewheels, running at about 5 MPH. The attached photo shows the 19ft-3inch sidewheeler Margaret S., underway at about 4 MPH, displacement just over one long ton, and total shaft power a little less than 0.6 horsepower. In my view this is entirely satisfactory performance for the boat’s intended purpose. The Margaret S. hull is much stronger than what Jeff might want, and the build process is documented on Thesteamboatingforum.net under “plywood sidewheeler building”.
While the Margaret S. is a steamer, I have also built an all-electric inboard boat at very low cost. Yes, amateur designers (as well as professionals) can work up a propulsion system with costs far beyond what might otherwise be found, but that problem is solvable by getting the proper engineering background to design the machine properly.
For Jeff’s application, simple belt and chain drive from a 1 horsepower electric motor for each stern wheel will work just fine. The main drive shaft can also be fitted with a lawn-mower type gasoline engine, which can drive the setup without electric use. The same setup will allow the gasoline engine to charge the batteries, with or without the paddlewheels operating. The proper drive motors will also be acting as generators to charge the batteries when the gasoline engine is running.
As far as costs go, again one can hire a high-end yacht designer and pay thousands just for preliminary design sketches, and hire Eaton Transmissions to design the power transmission system that costs $20,000 just for the design effort. But just because these choices exist, they are not the best choices.
I put together the 3/ 4 horsepower electric propulsion system for a 14 foot skiff at a cost of a few hundred dollars, including the deep cycle batteries, switchgear, electric motor, belt/chain reduction system (1750 RPM Motor, 400 RPM prop shaft), drive shaft and 14 inch bronze propeller. Yes, this required a lot of DIY work, but nothing more complicated than what any lawnmower repair mechanic would be capable of, and no tooling beyond what many homeowner’s basement shop has. In a pinch, an electric drill and hacksaw can do the whole job. A full description of this build can be found on the Yahoo ElectricBoats Group. This electric inboard ran without problems for 5 years, and I am now converting it to a fast steamer.