A buddy of mine uses these tie down systems to haul his very expensive Old Shelby Mustangs he likes this system and I think it may be a solution for you too. (Maybe not I just remembered your tight quarters, you may have a heck of a time tying that car down.
Travel Lite lockdowns
You may have to think about a winch, spool out a bunch of cable, then hook up the car, then winch it up into the truck tight against some custom built chock blocks for the front tires, then ratchet strap the rear down and into place.
blizz