I'm thinking a set or two sets of rubber wheels on axles which wind ropes over
pulleys to lift the top and suspend it over your car, under the door. Would need a neutral/drive shift so when you want to open the door but lift the top.
Never have seen a top. Can you lift one end at a time by yourself or does it have to be lifted straight up?
If you can lift one end at a time and it has hooks that you can attach to rope loops from the ceiling, then lift the other end?
That's how I hang my extension ladder in the garage. I'll probably lie awake all night working on this! Good luck.