I went to UPS and bought a box that fit. Mine was 3 inches from top to bottom, and about 4 x 8 inches. Then I went to Hobby Lobby and bought two pieces of foam, but of different stiffnesses. The bottom layer was 2 inches thick and stiff, more like styrofoam, The top was about 1 inch thick and was true very soft foam.
I traced the shape of the car on the bottom layer, marking the spot for the wheels as well.
I drilled four wheel holes similar to what I did for normal cars. Plus two more smaller holes in the middle of the car (for the fingers to go to pull the car out of the bottom layer).
Then I used my router (actually, I put a router bit into my upright drill), and routed out the shape of the car down to the depth that left only 1/4 inch space between the wheels and the bottom of the box..
Insert the car, lay the soft foam on top, ergo you have it.