We present a method for end-to-end learning of Koopman surrogate models for optimal performance in control. In contrast to previous contributions that employ standard reinforcement learning (RL) algorithms, we use a training algorithm that exploits the potential differentiability of environments based on mechanistic simulation models. We evaluate the performance of our method by comparing it to that of other controller type and training algorithm combinations on a literature known eNMPC case study. Our method exhibits superior performance on this problem, thereby constituting a promising avenue towards more capable controllers that employ dynamic surrogate models.