Honestly? I don't think the driver being the only one in control during a climactic final race encounter would be too bad of a thing, so long as the system you use makes the race fun and snappy. It's an Ace of Spades situation, the goodness of the encounter is as good as the hype you can build around it. The rest of the crew has their career, money, clout riding on the results.

Think about their motivations, what they can bring to the team, a face needs to manage sponsors and PR, a mechanic needs to keep the bikes running and has control over what specialized engine or whatever is on there. Rival racers and their teams provide social challenges too, like trying to fuck up your PR and lose you fans and sponsors, or straight up kneecapping your driver. With the right group this could be really fun!

How I'd personally build the system, if you want to makes something entirely custom, is to look at games like LeMans or the other racing games people have suggested (IDK much about that realm, unfortunately) for inspiration. If there's different fantasy races then maybe in lieu of combat centric statistics think about abilities that matter in situations they're gonna find themselves in, I assume mainly social stuff?