I would cut strips of backing and batting a ittsy bittsy wider than the rugs. Pin or use adhesive to secure the rugs onto the strips and do a continuous zigzag or serging. Do the other side. Cut apart and chain feed them through the zigzag process. Crank your zigzag down to almost a satin stitch or what your machine is comfortable with. I did twenty five postcards this way in an hour and the quilting group was so amazed. Uh, you did ask for suggestions, not opinions?