Take a close look at existing linen and poly strops. How are you planning to duplicate the seamless look? If you do any sewing of a tube and invert it you will still have the edges just enough thicker than the body of the strop and that will not give you the flat surface you need for effective stropping. If you use it without some kind of edge treatment you will have continual raveling of the edges, even with thicker fabrics. Contemplate finding a glue that you can then layer fabrics with without stiffening it too much. That at least would solve the edge problem. Also check the weave structure of the old ones to get an idea of what to look for texture wise.