Heterogeneous 6G radio access networks (RANs) must allocate resources reliably under interference, latency limits, imperfect channel state information (CSI), and architectural diversity. We propose a degeneracy-aware resource allocation (DG-RA) framework that casts multi-architecture orchestration as a probabilistic game and, unlike single-solution optimization, deliberately favors allocations realizable by many structurally distinct yet performance-equivalent strategy profiles. Resilience is quantified across three layers through Degeneracy-Weighted Path Robustness (DWPR), Functional Substitution Score (FSS), and an Algorithmic Resilience Quotient (ARQ). Across centralized (C-RAN), open (O-RAN), virtualized (V-RAN), and hybrid RAN architectures, and benchmarked against a fractional-programming optimizer, DG-RA matches the state-of-the-art throughput and outage at the static operating point, then exploits its equivalence set to recover $\sim$$99\%$ of throughput from a resource-unit failure with a single switch, where a single-solution optimizer needs tens of iterations to re-converge. The results recast degeneracy not as a rate booster but as a precomputed resilience reserve for disruption-tolerant 6G orchestration.