I also did some Monte Carlo tryouts until running out of time. I had a model with a target point for each pod in game, and I assumed that each pod would accelerate towards that target for at least a certain amount of turns. For runners, this was usually a point near their next checkpoint, for blockers they usually targeted somewhere near the other runner.
For the enemy pods, I predicted these target points either from the intersection of the acceleration vector of the previous turn and the one of the current turn if there was any, or an arbitrary target point 5000units ahead in the direction of the current acceleration. Also, during the turn prediction, if I detected that a blocker was near my runner, I assumed that it would target its (position + speed + acceleration) point.
To choose the best move, I selected a random target point for my pod, in 5000 units around its position, and a random thrust value, and I simulated an acceleration towards it for 10 turns (I did some experiments with more or a random number of turns but it wasn't more effective). For each turns, I predicted the whole system, including collisions, and the enemy supposed trajectories, and evaluated each trajectory with different evaluation functions depending on the pod strategy.
I wanted to evaluate the moves of my two pods simultaneously but couldn't manage to get good results. So I evaluated my blocker strategy first, with the evaluation function trying to maximize the distance of the ennemy runner to its next checkpoint, with penalties when it reached it, as well as the proximity of the blocker to it. The runner evaluation was the opposite, trying to minimize the distance to the next CP, with bonuses when passing through it and for proximity to the checkpoint after it.
I guess it wasn't too bad, but that's probably because I did it a lot of time...
Regarding the shield usage, I had it initially as a randomized parameter, but I finally moved it just before outputting the result, and activated the shield every time there was a collision going to happen with 100% certitude, except when the collision was on the runner and from behind. In the end it was pretty effective to kick other pods out of my way.