Routing in satellite constellation networks with inter-satellite links has become an important aspect to enable broadband Internet access and to integrate into terrestrial networks. However, their dynamic characteristics and large physical size require specifically tailored solutions. To address these challenges, we propose and investigate a load-balanced routing protocol based on distributed software-defined networking. The approach relies on independent space-borne clusters with on-board controllers. Reduced signaling overhead is achieved by geographical inter-cluster routing algorithms. We evaluate the performance of the protocol in a custom-built system-level simulator, considering different architectures, design choices, and scenarios. Comprehensive comparisons with source-routed schemes and an upper benchmark demonstrate the viability of the solution. Notably, for the given scenario, the protocol handles network loads 97.4% higher than source-routing before quality of service compliance falls below 95%, while maintaining an average routing convergence of 117.338 ms . The work provides valuable in-depth insights into the design of optimized routing protocols for satellite constellation networks.