Prism99

One thing I do to forestall this kind of problem is mark the cutting line on the quilt (with a permanent Sharpie) instead of actually cutting the quilt. I use that line as my "virtual" edge when applying binding; this would also work if you want to apply a basting line around the quilt first. I cut the sandwich *after* the binding is applied (being very careful not to cut any of the binding at the corners!) This helps a lot because I am not struggling to keep an edge under control; I just match the cut edge of my binding to the "virtual" cut edge of the quilt. Cut edges are more easily stretched and distorted with sewing; this method keeps all layers completely under the presser foot and also completely covering the feed dogs.

Another thing that helps prevent the issue you had is to heavily starch the backing before layering the quilt. Starch stabilizes fabric so that it is much less likely to stretch and distort while sewing. I use a large wall-painting brush to apply a 1:1 solution of Sta-Flo liquid laundry starch and water (this is a very heavy starch solution) to the backing, wait a couple of minutes to make sure it has saturated the fabric fibers, toss in the dryer, then iron with steam. I haven't tried this with a tied quilt, but I don't think it would interfere with the tying process.

Yet another thing you could do with a tied sandwich is use Elmer's washable glue to glue the entire edge down before sewing on the binding. That would be fairly time-consuming, though. Basting spray would be faster but much messier, although there is a newer web-like basting spray that might work.