Another idea (which I frequently use) is to put fusible batting on the back of the backing fabric (your red check in this case) and iron it down NOT using steam, starting in the center and working, with your iron, outward. This will give stability to your background fabric and it also gives a nice outline to your figures when you use a small applique stitch to put thim on the backing. For an extra 3D effect you could put your figures on to the same type of binding. You'd have to widen the size of you applique stitch, but it would add to the bang of the entire quilt. There are a lot of choices of bonded batting out there, but for this I'd use a flat style. It will be stiff, but when you wash it all that stiffness comes out and leaves a nice soft quilt.