ahhhh, I see what you mean. If it were me, I’d weld some rails in under the body (like a ladder bar that clears the frame) and use that to lift it (use 4 chains in the corners going to the crane). I’m not familiar with those cars though nor the equipment you have available, but if you get creative, it shouldn’t be too bad.
EDIT: and if you have the steel stock laying around, maybe even build a dolly to rest it on once it’s off the frame so you can wheel it around and whatnot.
gl with the project