Cooperative gene regulation often depends on groups of regulators acting jointly, but most gene regulatory network (GRN) inference methods output pairwise regulator-target rankings. We introduce Bottleneck-Aware Regulator-Set Inference and Diagnosis (BRIDGE), a framework for complete regulator-set recovery, and Targeted Recovery Attribution for Cooperative Evaluation (TRACE), a diagnostic suite that attributes failures to retrieval, set-level scoring, decoding, and evaluation bottlenecks. TRACE includes a leak-free mechanism-mismatch cooperativity stress test in which cooperative targets are generated by random nonlinear mechanisms rather than product interactions. This design avoids feature-mechanism circularity: Residual higher-order set scoring (Residual HOS2) operates on raw expression vectors without handcrafted product-correlation features. Across 30 matched seed-cooperativity settings, Residual HOS2 improves Jaccard similarity from 0.382 to 0.460, recall from 0.522 to 0.597, and exact recovery from 0.053 to 0.113 over a decomposable pairwise set scorer (PairS2), although exact recovery remains low. On SERGIO DS3, oracle retrieval and TRACE show that candidate coverage is necessary but insufficient because set-level misranking remains the dominant source of exact-recovery failure. PairS2 proposal followed by Residual HOS2 reranking reduces HOS2-scored candidate sets by 94-97% while largely preserving exact-recovery behavior. These results distinguish edge ranking, candidate retrieval, set-level scoring, and exact cooperative regulator-set recovery as separate objectives.

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