The increasing density of many-core architectures necessitates interconnection networks that are both high-performance and fault-resilient. Eisenstein-Jacobi (EJ) networks, with their symmetric 6-regular topology, offer superior topological properties but challenge traditional routing heuristics under fault conditions. This paper evaluates three routing paradigms in faulty EJ environments: deterministic Greedy Adaptive Routing, theoretically optimal Dijkstra's algorithm, and a reinforcement learning (RL)-based approach. Using a multi-objective reward function to penalize fault proximity and reward path efficiency, the RL agent learns to navigate around clustered failures that typically induce dead-ends in greedy geometric routing. Dijkstra's algorithm establishes the theoretical performance ceiling by computing globally optimal paths with complete topology knowledge, revealing the true connectivity limits of faulty networks. Quantitative analysis at nine faulty nodes shows greedy routing catastrophically degrades to 10% effective reachability and packet delivery, while Dijkstra proves 52-54% represents the topological optimum. The RL agent achieves 94% effective reachability and 91% packet delivery, making it suitable for distributed deployment. Furthermore, throughput evaluations demonstrate that RL sustains over 90% normalized throughput across all loads, actually outperforming Dijkstra under congestion through implicit load balancing strategies. These results establish RL-based adaptive policies as a practical solution that bridges the gap between greedy's efficiency and Dijkstra's optimality, providing robust, self-healing communication in fault-prone interconnection networks without requiring the global topology knowledge or computational overhead of optimal algorithms.