Sadly, I don't think there is a simple way to replace the lines with arcs, at least not in a way that would be more efficient than using more iterations.
Using a couple hundred iterations doesn't take that long (It renders in less than a frame) and doesn't look that bad, anyways.
Nice work. I've written my own code to draw n-order beziers since since back in PTC (I've since ported it) and we seem kinda similar. Maybe we should compare? ;)