Moving block railway systems are the next generation signalling systems currently under development as part of the Shift2Rail European initiative, including autonomous driving technologies. In this paper, we model a suitable abstraction of a moving block signalling system with autonomous driving as a stochastic priced timed game. We then synthesise safe and optimal driving strategies for the model by applying advanced techniques that combine statistical model checking with reinforcement learning as provided by Uppaal Stratego. Hence, we show the applicability of Uppaal Stratego in this concrete case study.