Regarding the walking foot, why not check with the insert that came with yours? Mine says if my stitch length is at 3 or below, I can reverse stitch. I think it all depends on the brand you are using. I personally won't take anyone's other than the manufatcurer's words for what I can or can't do with my sewing machine and accessories, lol.
A friend was telling me about doing the binding completely by machine, and I tried it on a small quilt for the first time and it worked nicely. Attach the binding in the back of the quilt, turn your quilt over and use a washable glue to glue down the binding on the front, then use your favorite stitch to secure it down.
Good luck.
ooh, I also meant to say that I don't reverse stitch when quilting, rather, I take a few very small stitches at the beginning and end.