I agree with the starch, starch & more starch. Also lengthening your stitches. Also, if you can adjust the pressure on your presser foot all the way up to 0. If that fails, just machine tack it or tie it.
I like puffy battings but my quilting machine absolutely refuses to work with them. It just doesn't have enough clearance and tries to bulldoze through. I have to cover the quilt with tissue paper and quilt through the paper.