I always prewash and dry flannel *and* starch it heavily before using. The prewashing and drying take care of the extreme shrinkage that often happens with flannel, and the heavy starching keeps the flannel from stretching as I sew.
Perhaps you could get a heavy spray starch and starch the backing fabric even though it is already sandwiched? I have to be careful with spray starch because I always seem to have overspray, plus I tend to keep my iron so hot I scorch the starch when I iron. However, it might be worth doing some careful experimentation with spray starch to see if you can stabilized the flannel without taking the quilt sandwich apart.
Oh, and I no longer do SID because mine is always uneven and I don't like the look of it. I think it is much easier to do gently curving lines with the walking foot. There is no need then to watch the ditch like a hawk, and I like the softer look of the wavy lines.