The only thing I can think of is purchase a blanket instead of batting. I would go with a thinner manmade fiber, then add your top, no backing needed, although you can add one if desired. The blanket will not need to be quilted at all, just cut it to the desired size and bound. The only difficult thing would be to make sure that the top is smooth on the blanket. I would lay the center portion on the blanket and baste around the edge. Lay this in-process piece on the bed to ensure that the drape is correct and adjust as necessary. When you are happy with this part, add your borders with the sew and flip method, trim the blanket to the correct size and bind it.