I think you could use the walking foot the same way as any foot for the corners - sew to the seam's length away from the corner (usually 1/4"), remove the quilt from the machine, fold the binding up at a 45 degree angle, fold it down square with the side you just sewed, sew from the top to the next edge and repeat.
You don't have to remove the quilt from the machine when you get to the corner. Just sew from that point, 1/4 inch from the edge, or whatever seam allowance you are doing, to the very corner on a diagonal. Leave your needle in the last little bit of fabric in the corner. Lift the presser foot. Turn the quilt to come down the next side. Fold the binding back, slide up, and fold down. Then lift the needle and move over to the place where you want to sew. Lower presser foot and away you go down the next side. No cutting of thread at the corner!