Seems really straight forward to me! So example of play with the new system would be like...

[quote]Player 1 has TAL level +3, so they roll 3 extra d6 to accelerate past the pack. 4d6 resulting in rolls of 2, 4, 4, and 5. They have three successes versus one failure, and no bonuses or malfunctions, so they succeed in their action. Player 1 writes their post out in more detail and ends with them accelerating past Player 2.

Player 2 rolls their 1d6 reaction to maneuver in front of Player 1 and stop their advance. They roll a 2, so they fail and take chip damage. They write their own post on their attempt and failure, their character's frustrations, etc.

Repeat for each player, then move on to next round/lap.[/quote]
Do I more or less have it?

If you're happy with it, I think this is a very easy to understand dice system. To help you establish it a little more, I have some quick questions for you. 

1. If a player is rolling an even number of dice and gets the same number of successes as failures, how would you handle that? Would it count as an overall success?
2. For damage, especially reaction damage, is the d6 rolled again or would it use the same roll as the reaction? Like in the example above, would Player 2 take 2 damage or would they roll again to see how much damage they took?
3. How do malfunctions and bonuses interact with each other? Let's say if Player 1 rolled 1, 4, 4, 6. My assumption is that they would succeed, go farther than normally possible because of the 6 (like maybe move up 2-3 places instead of just 1), but their vehicle sustains some damage from being pushed too hard because of the roll of 1?

Over all though, I think this will work well for a simple system that players flesh out the results of with their writing.