If you want to "re-body" the car, changing the VIN plate and all (which is very illegal in some areas), then why not just get another car and start over? Not bothering with "changing the numbers" to match your existing documentation. For ultimate value, if that matters, you WANT a clean title, not a "reconstructed vehicle" sort of situation.
As for the "nobody will know" orientation, the reason there are so many VIN-related numbers on the cars was so that "chop shop" operations could be shut down. Where they'd steal the car for its parts (other than just the drivetrain), for resale.
In TX, removing a data plate from the body of a '60s Mustang (to paint under it, at a noted restoration shop) got the shop owner in trouble with the stolen car detail. One Mustang with the data plate and VIN removed, as it was a race-only vehicle, was confiscated and not returned. With no VIN, then ownership could not be confirmed. ONE BIG MESS! Lots of money spent, just for the shop to stay "clean". Lessons learned. Perhaps they didn't find what they might have been fishing for? Who knows. Sour grapes from a former employee? Anything's possible.
So, all of those "hidden numbers" on the body were a part of a concerted vehicle anti-theft movement by law enforcement, aided by the OEMs. From the later '60s and continuing into the '80s (and later).
So, getting a more solid parts car shell would be the only option, it seems. Where sections of metal could be transferred from rather than custom fabrication. Some of the floor pans and trunk floor can already be in repro (or reasonable facsimilie) from a few sources.
Check out the several threads in here on common rust areas of the Fuselage cars and how others have repaired them. Quite interesting!
Just some thoughts,
CBODYT67