I would sew it using a 1/2" seam allowance starting at the very edge just like you made the 1/4" seam allowance. It will take up some of the extra width of the binding and when you flap it over it will be a bit narrower. Don't pull it off, too much work and it will distort you quilt edges.
Ideal width of a bindng is 2 1/2" if you are using a low loft batting. That's what I use and my binding is perfect all the time. Good luck.