Another update:
Mr Carsons collection of documents revealed that the board of Birkenhead Improvement Commissioners were worried about the potential damage to paddle wheels both during docking and occasional groundings so they were investigating different designs involving fully enclosed paddle wheels.
The experimental designs involving twin hulls and a central paddle wheel had proved unsuccessful and this type of design didn't offer any protection to the wheel during grounding.
The board were very interested in parts of the American design, namely the water inlet / outlet systems and the interaction with twin paddle wheels whilst enclosed within the hull.
They requested the shipyard to produce outline designs for such a ship which included a basic model.
I can't say for certain that the builders model that Dave photographed is the same model but it demonstrate all of the design details that a potential customer would be interested in.
The documents also contained rough concept sketches of the vessel which I am busy interpreting into meaningful drawings to see if the internal paddle wheel version could have ever been built.
Paul