Originally Posted by Jan in VA

Why not trying making your binding wide enough to be your narrow border?

Cut it on the bias as you would any bias binding.
Cut it 4.5" wide, fold in half, sew to the BACK with a 1/4" inch seam at the edge of the backing and batting that you have trimmed to the finished size quilt you want.
Fold to the front of the quilt, covering the batting that is about 1.5" wider than the finished top, and sew down right near the edge of the pieced top.

The bias will allow you to get around the curves.

Jan in VA