I too remove the seam pieces earlier....at least on the "inside" of the pressed seam so it doesn't get caught in another seam underneath.
Honestly I haven't had a hard time and do suggest a smaller stitch and also "crinkling" your quilt top up a bit to help loosen some of the papers/seams. Most of mine actually have some pieces falling out on their own as I piece and rarely do I have a spot that isn't easy to pull out.