You can just use the bias binding on the curves. It takes a little preparation to peice the bias in the right places but it works beautifully. I have done this and it is worth the prep time. Straight of grain does not really play well on curves and it would be a matter of having to re do it when it doesn't work out the way you like. So time spent in the beginning is better than time spent re doing.
Tartan has the right solution.
Be sure to post pics for us to enjoy.
peace