Basically, you need something to lift a 400 lb weight while you’re removing it from the car - a forklift arm or similar.
I did add some documents on them to the vehicle parts on the wiki: http://cddawiki.chezzo.com/cdda_wiki/index.php?title=Vehicle_parts
Basically, you can use a telescoping cantilever or boom crane if you have one, or craft a pallet lifter from pipe and a bottle jack, or install a frame on a frame to act as a forklift arm.
I generally prefer the telescoping cantilever in the early game - it’s foldable, provides jacking and as well as lifting, and is surprisingly easier to make than a pallet lifter even though it’s more useful. Build two folding frames, install a folding shopping cart basket on one of them and the cantilever on the other, and some castors, and you’re set to go around and steal storage batteries and reinstall them in your home base/deathmobile.
Late game, you’ll want a boom crane to change the tires on your deathmobile anyway, but it doesn’t fold so it’s not as useful for quick looting in the field. You can install it on a nearby vehicle, scavenge parts, and uninstall it and take it with you, but that takes a fair bit of time and isn’t that great a solution unless you really need a couple more 24" armored wheels.