Binding is the finish of all your hard work ... but it is not my favorite part either. I think your idea of using multiple fabrics for the binding is great. I, personally, would use shorter strips, like 18" or 20" of each fabric, and seam them together with a 45 degree seam into a long enough strip. Then measure carefully so that you are not ending on a corner or with the same two strips together at the end. You may have to fudge a little at the end but it will look very nice with your quilt.