I too would advise changing from safety pins for basting to either basting spray or Elmer's glue. Think about spray basting. When you use this, all three layers are continuously "glued" together. With pins, no matter how closely you pin, the three layers touch only where the pins are. No matter how careful you are, each pin is bound to take up a little more or a little less of one of the layers. For basting, you really cannot beat having continuous contact between layers.
Another thing that helps tremendously, even if you pin baste, is heavily starching the backing fabric before layering. Starch stabilizes the backing fabric so it is much less likely to stretch or move as you handle it. I recommend a 1:1 solution of Sta-Flo liquid laundry starch and water (the heaviest starch I have been able to use efficiently). What I do is "paint" this solution onto the backing fabric using a large wall painting brush (the kitchen island works great for this job), wait a couple of minutes to make sure the fabric fibers have had an opportunity to absorb the starch, toss in the dryer, then iron with steam.