How did you apply the backing and what fabric did you use? Did you use batting?
Is the quilting stitches you referred to necessary to hold the piece in place (no sagging)? What thread did you use for this quilting stitch?

I’m thinking about trying to appliqué my piece to wool felt using invisible thread. Then doing stem stitching around edge so the backing will have only a frame on it. Was thinking felt would add a little stiffness to it. What do you think?