Trans-Am info for the 1966 Barracuda
On this side the pond, FIA solved the problem of originality by introducing Historic Technical Passport (HTP). This means that basically there is no requirement of any originality, as long as the car is technically according to the period specs. So for example you can convert an ordinary Ford Cortina to a Lotus Cortina (which was actually done in period as well...), or make a GT40 even from old shovels, as my good friend said... :D
There are pros and cons in this approach. It stopped the tricky playing with the orignal papers and chassis numbers, but it also meant that new "continuation" cars were brought to races. These are built from scratch today, with no real history at all. The development now seems to be that the original cars collect dust in museums while the newbuilds are raced.