You might find it interesting to install and try both Huub (https://github.com/huub-solver/huub) and Pumpkin (https://github.com/consol-lab/pumpkin) as well. I have both in https://zayenz.se/blog/post/benchmarking-linkedin-queens/ with good results for the small problems I tested there. Both also did very well in the MiniZinc Challenge this year.
One thing that might be interesting (and might be useful for some solvers) is to change from checking if there is a solution and requiring each part to be used in the solution, to find solutions and minimize the number of unused parts.
One additional constraint that you could add that I don't think I've seen is distance to goal. In essence, for each grid position (without considering any tracks) there is a shortest time it would take from that position to get to the final position. If a train is in (a, b) and would take at least time t to get to the exit, there is no way to solve the problem if it is in (a, b) at time MAX_TIME-t. Might be useful for some solvers, worth testing.
Finally, adding some simple heuristic might help some solvers (I'm thinking of Gecode in particular here). My initial guess would be to add an interleaving over time steps of the train_row, train_col, and train dir for each train and search in order. That would as a basic heuristic represent a search from the start snaking out. Value choice is trickier to specify in MiniZinc of course.
