a (stay stitch) all the way around the top before quilting (just a straight stitch- in a little less than 1/4" all the way around a top with bias edges) will help stablize- keep the top from stretching- while quilting/handling. dense quilting will (stretch) the bias edges more- a more open quilting design will allow (some) easing in-
stablizing first will help the most-
good luck-