Maybe if you wrapped a length of the exhaust with a coil that heated vegetable oil and fed into a small resevoir you could use this heated oil as the expansion side of the engine and use some fins on the air cooled vacuum side.

Then the stirling engine could keep running even when you are done riding and could then charge the batteries over a longer period of time.

Running the stirling engine on a shimano hubs an idea I've kicked around awhile. But I've only worked with beer can engines myself and have yet to make that much power, but I've seen engines that could and would probably benifit from one.

These engines get pretty big and make little power to size, but , it really aint that necessary to make huge watts when these batteries will only absorb so many watts per hour anyways. Maybe a smaller output but long lasting and "FREE" generator would be good? interesting.

Cool idea... last one I thought I'd see here but you made it apply. Rock on.