If you take the sandwich apart, I would also heavily starch the backing fabric before layering. I use a 1:1 solution of Sta-Flo and water. This will stabilize the backing fabric so it doesn't stretch and distort as you quilt. I would also spray starch the top as heavily as possible.
Also, if your machine has a means of regulating the presser foot pressure, you may want to try lightening up on that. Your machine's pressure is probably set for sewing two layers of fabric together; with a batting in there, it may be heavier than you need. That would also create "drag" on the quilt layers and perhaps stretch the fabrics.
Oh, and spray basting is a good idea too. I have never had a problem using 505 with a starched backing fabric.