I doubt that I could piece in the fabric and get it to lay flat. I think that I would buy background fabric as large as the star. Then I would lay the star on the full piece of fabric and gently press outward from the center and pin down the star. Then I would top stitch out from the center in all eight direction up to the inside diamond shapes. I would then see if the diamond points were still laying flat, if they were I would applique bias tape in blue or white over the raw star diamond point edges. If it still looked good, I would make my quilt sandwich and quilt the heck out of it. Good Luck!