Last car I scavenged down to the frame, I bolted a pair of 1,000 lbs castors to the underside of. If they are set at or near the tipping point of the frame, it is surprisingly easy to move the car around. When the scrapper comes, tell him he needs a tilt & load flatbed or 4-wheel dolly. He'll hook the winch to it, and the car won't have much choice but to go (try to salvage your castors).

If you are planning to scrap the car yourself, rent a flatbed trailer, tip the front of the car up onto it, use a come-along to pull the car forward as far as you can, then lift the back with a jack, get 3 guys lined up across the rear and give a good shove to get the castors onto the tailgate. Once the castors are up, you can roll the chassis forward. Jack the back up on the trailer, remove the castors, and drive away.

Since the car is scrap at this point you don't need to be gentle with it, but you don't want to tear up your driveway.