Effective routing in satellite mega-constellations has become crucial to facilitate the handling of increasing traffic loads, more complex network architectures, as well as the integration into 6G networks. To enhance adaptability as well as robustness to unpredictable traffic demands, and to solve dynamic routing environments efficiently, machine learning-based solutions are being considered. For network control problems, such as optimizing packet forwarding decisions according to Quality of Service requirements and maintaining network stability, deep reinforcement learning techniques have demonstrated promising results. For this reason, we investigate the viability of multi-agent deep Q-networks for routing in satellite constellation networks. We focus specifically on reward shaping and quantifying training convergence for joint optimization of latency and load balancing in static and dynamic scenarios. To address identified drawbacks, we propose a novel hybrid solution based on centralized learning and decentralized control.