As a parent, I should have known that if I made a toy/game for one kid, I'd have to make something completely different for the other. My son is currently a big fan of racecars. I quickly mocked up a 1930's - 1940's US roadster and dropped the bear in.
The entire roadster currently fits in a 1.25" x .75" grid. This seems big enough to put enough spaces on the table and still have a decently large movement piece. The car has a 1/2" square hole where the bear sits. This would (theoretically) allow bears to change cars. Possibly players could sell cars and/or hire different racers to drop into their cars.
I'm floating between two rough ideas for the game itself. My first thought was to take a game like Chariot Race, Ave Caesar, or Charioteer and adapt it for early roadsters. Racers would roll speed and control dice based on base scores and their current gear. Successes on speed dice allow the car to move forward. Control dice would allow a car to change direction as part of a movement.
The other idea is to create a "never ending straight away" race track where as players complete a segment, a new segment is added to the front of the board. Segments would be filled with obstacles, bonuses and surprises. The board would be similar in mechanics to Thunder Road: Vendetta, but much more silly.
The benefit of having the complete circuit as part of the starting condition of the game is that it allows cars to make pitstops. I imagine that both game ideas would have cars receiving damage and becoming slower, less maneuverable, or less controllable. A multi-lap race gives players at least a few chances to make pitstops. The never ending straight away allows for more customization in game length and would allow more creative obstacles/events to be added as the players become more advanced.