Personally I really like how Savage Worlds Adventure Edition handles Chases, the rules for those are pretty nice and open-ended, allowing for combat or pure racing. If you need it to go quicker, you can do what it calls "staged encounters", which is basically a vingette where at each stage of the race you present a problem, ask how the players will resolve it, and determine how well they do with a single roll of the appropriate stat/skill, then you divert them along one path or another based on how well they did and/or what they did.

Anyway I find those rules are generally adaptable to basically any system

Do you have long action mechanic? A classic way for chase is to stack success until you reach a threshold, in that context cheating is a way to use other skills than drive/run to gain success.

To answer my own question, based on all the responses, thank you everyone, here’s what I’m thinking.

Get a number of different colored d20s, one for each race team. At each leg of the race roll them all on the table for the players to see. Any 1s are automatically knocked out of the race, they had some catastrophic failure. Any 20s get a marker to indicate some great success or inherent skill that will grant them a bonus later.

Then in the final portion of the race I’ll take the three teams with the most markers and put them in scene in direct competition with the Players. I’m thinking this will allow my Player’s to go hunt teams that are doing well to take then out before the final leg if they want and let them see how dangerous their competition is.

I would treat it as any other situation PCs don't control - as a story

Instead of rolling or resolving anything prepare a bunch of occurences that would make you feel the setting you are using. And depending on the flow of the story ATM, either choose the more dramatic ones or the more mellow ones

If you don't want to run it purely as gm fiat, prepare some random tables per node and roll when the nodes are in their sight

Haven’t tried it myself, but Wylock did a video on the mechanics of his own Neon Skies:

https://youtu.be/LlPeZI4ctvE

Only once or twice. I play it like combat. Every racer plays in initiative order and has a set of available actions and resources.

With twenty other racers, that sounds tedious to run. I'd be lazy and say the players, their nemesis, and a couple of other racers pull out ahead and hand wave the others out of the scene.