Alex Anderson told me a few yrs ago that sometimes the problem is a lot of quilting in the middle then less quilting on the edges or border. I know you don't have a border....in that case, I definately stay stitch the edges (no stretching when doing it either) Then measure thru center of quilt both ways and add binding.
The quilt I asked Alex about has to have the border taken off and start over from there, with lots of hand quilting. I'm just sick about that but I will eventually do it.
A quick fix for you is to put a rod pocket on the bottom and just get a dowel to flatten it out while it's hanging.