I think you have a very well thought out plan already.......some seat time in a school wouldn't hurt , but probably isn't a necessity.
Work on establishing a routine regarding each phase of the run.....like anything else , it becomes mechanical. Next thing you know , you're actually good at it........except a golf swing for some reason.

I like the go kart idea......they are nimble and require very quick reactions to make them go fast. There used to be an indoor track up your way ( Blaine ) that had some quick carts......if they are still in business , I'd start there.