This doesn't take long, you do the intro race and then you play the first 5 or so races and you're done.
The way it works is once you've crossed the influence threshold you qualify.
For an easier time you do far better for influence finishing in the top 3 so it may be worth cranking the difficulty down to speed this one out.
If you have the treasure map, you could probably do this very quickly just using the influence boards as an alternative.