Cool concept might want to tweak the speed imo.
Unless im misunderstanding, by the math the Train player almost cannot win with a speed cap of 3 and a random start speed unless they are playing without an opponent.
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You're right, it can win but it's unlikely. With full speed for 5 moves (4 turns + initial move) it would move 15.
I moved stuff around while writing this down and I missed the new math. A 5th turn would bring the average speed needed to 2.1, which is much more obtainable. A max speed of 4 would be cool too, but it might be too much in favor of the train.
Train's health too might need adjustments.