I would say "yes" to adding after quilting to the edge. Remove the binding and save it as you may need it later (for facing).
I made a quilting for my great-granddaughter and had it quilted on a long-arm. The edge called for prairie points. After squaring the quilt, I added them to the outside of the quilt using a 1/4" seam. I added a bias facing piece to the back of the quilt. I trimmed as closely as I could to the stitching, pressed toward the facing, turned under the edge and then hand stitched.
I had used 30s fabrics for this quilt and cut the facing from all of the fabrics used which added a bit of charm to the back. I was very satisfied with how it turned out.
Suzanne