Seems like it would be fine (parody laws apply). It’s done similarly in the Saints Row games, with parody names which sometimes are obvious, other times need a little thinking. The cars are all generic with some resemblance to the models parodied. If your cars are very cartoonish and deformed I suspect you’ll be entirely in the clear.
Double-check with relevant laws in your region etc. Can’t see anyone but the dumbest attack lawyer finding a problem with this though.
Never rely on common sense to determine whether or not something is legal or not in copyright – it assumes that copyright law was invented with some kind of common sense involved, when, in fact, the drafting of copyright and patent law was done in a dark room where all forms of common sense, creativity, emotion, and imagination were strictly banned, and the committees involved chose members based entirely on who had the fewest possible emotions and facial expressions.
Copyright law is completely independent of common sense and the only way to tell whether or not something is legal is to look at the books, leave logic at home, and devolve into insanity.
That being said, you are right – as long as David does not use any trademarks or logos purchased by the car manufacturers or anyone else, the works are legal.