Not a movie, but a TV series called Wind At My Back, that my 97 year old mother-in-law watches daily. Lots of Model A's there.
The previous owner of my 30 fordor had that car in quite a few movies. From what he had said, he put his name on some list, and if they had a need for a car like yours in your location they would call you with an offer. He told me it was in the movie The Godfather, and they dressed him up to look like a gangster and actually let him drive the car. How cool is that. He still has a big grin on his face everytime he tells that story.