For starters, you have not identified just what is rusted out. Frame mounts on most of our cars are toast by now. Not difficult to fix. You will not know the full extent of the rust problems until you disassemble the car. Typically you can expect rust damage at the lower portion of the front fenders, lower front on the doors lower rear quarters and wheel wheels, floor pans and possibly the lower cowls.
It's hard to believe the rolling shell for $1500 has no rust issues.
I would not screw around with the VIN's. Document what you have done and take off the VIN of the donar car and put it in with your doc on the restored car. It's going to look better to be transparent with what your doing than trying to hide it. You could be risking loosing your car and/or fines or worse.
IMO
BTW, creating an ID in this forum which looks like a first and last name, and then ask about how to do something that is unlawful in at least some states is not a good start. When you click Submit it's on the internet FOREVER.
Engine Test Stand Playlist: https://www.youtube.com/playlist?list=PLwoxyUwptUcdqEb-o2ArqyiUaHW0G_C88 restoring my 1968 Firebird 400 HO convertible (Firedawg) 1965 Pontiac Catalina Safari Wagon 389 TriPower (Catwagon) 1999 JD AWS LX Lawn tractor 17hp (my daily driver) 2006 Sequoia 2017 Murano (wife's car) 202? Electric car 203? 68 Firebird /w electric engine 2007 Bayliner 175 runabout /w 3.0L Mercuiser__________________________________________________________