Well with any story line the vehicles will have to play background to the actual story - the human interest angle that makes the film watchable to a wider audience. You might want to check out 'Highwaymen,' which was not half bad. Think of the film as a Western and the cars are like horses - how much time do they really spend on the horse?
Vanishing Point was certainly a period piece so I would not try to copy that. Two Lane Blacktop is as well, but has more to emulate in how it was shot. Our cars are very sensory in nature, and you need to find subtle ways to bring that out. Two Lane had basically no background music so you were able to experience the rhythm of the car. American Graffiti was clever in that they used car radios as the focus of sound generation, and as cars entered or left scenes the audio would be manipulated and diminished.
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Here's an idea, how about a play on 'GTO' from Two Lane. Warren played a bit of an odd straight man against the crew in the chevy and most of the passengers that he picked up along the way. There was an editorial in maybe HP Mopar a long way back that described a friend of the writer, I believe his name was Frankie and he owned a Hemi b-body. I will never forget the description of Frankie and the only two shirts he owned, each said Hemi across the chest; one was dirty for when he was under the hood, and the other was clean for when he was driving. That is your lead. Have him travel in an attempt to find himself or America or whatever, and delve into his interaction with the current freaks of this generation.