If you are determined to quilt these quilts, you might try a quilt as you go but you will have to cut fabric and batting. You start with the center section (rectangle) then add strips of top, back and batting so when you open the seam out you have the next row quilted as you piece. The pieces can be as big as the batting allows you to be.
I know this doesn't make sense, but look on youtube for a quilt as you go video. Seems like I saw one there.