The pattern you link looks like it would be admirably suited to a quilt as you go method, which is basically what you outlined doing, except you don't have a solution for dealing with a loose and un-attached backing. I think you would find that the wear pattern of the backing would be affected adversely.
What if you were to quilt conventionally in 4 quadrants, then attach the quadrants together along the sashing area?
Whether this is worth it would depend on how you intend to quilt it -- straight line stitching? FMQ? Edge to edge or a motif? In the ditch only?
Another idea you could play with would be to do what you planned, but then also add tacking, tying, or a decorative button or area of stitching in the cornerstones of the sash to keep that backing from billowing.