Quite possibly, the latter sugestion would work out better. If you have a project coordinator, see if they can pick out a couple of spots along the way and find some of the locals to sponsor a car in the condition it needs to be in per the script.
Start out with the full car for the first 50 miles or so, and then in the next state, a business may want to get involved for the publicity and have a car for the next stage. Then someone in the next state, and so on. Let them travel for 25 to 50 miles with the show. This could very well establish more interest for the whole run.
Maybe a Pontiac dealer, custom shop, bone yard, local TV or Radio, car magazine, etc.
Just a thought.