Could you fuse it to a stiffer interfacing?
I know the ones I made for my boys when they were small I just quilted...and they loved them! My oldest son once asked if he could play with his cars on a double wedding ring I had for a wallhanging in our bedroom...just 9 rings 3x3....and he had more fun driving his cars around the rings. Every once in a while I would let him do that...as a reward if he had been especially good.