I like the idea of using decorative stitches!
What I would do is wash the satin and then starch it heavily before cutting (to stabilize it). My method is to mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this on the yardage using a large wall painting brush, toss in dryer, then iron with steam (although with polyester you might want to remove the yardage from dryer while still damp and use a cooler iron on it without steam). This treatment would make the satin much easier to handle, both for cutting and for piecing. I would probably cut large squares and use a half-inch seam (because satin ravels easily).
I really like the idea of quilting these squares to a flannel backing using decorative stitches. I would wash and dry the flannel a couple of times first, then use the heavy starching method on the flannel backing. I would spray baste the two layers together, then do the decorative stitching as the quilting method. Starching both top and flannel backing would practically guarantee no puckers, and the starching would likely eliminate the need for stabilizer.