I know you probably want to use up leftover strips for the project, but I think that if you wanted to start fresh on the project the ideal maerial for something like that would be to use bending birch plywood. Lee Valley sells "Finnish birch" plywood in smaller pieces.

You might be able to use up your scrap by cutting the strips into pieces about the width of your wheel and edge-gluing them to a round form, like you would building around a form for a kayak. Given the material you have to work with, I don't think that bending will produce the results you are looking for, but as long as you don't mind the facets I think this would, and it might look cool with the facets, if you mount them to round rings like that.

m