When Agent Governance Helps

No specification says how a governed autotelic AI agent organization, where agents pursue self-generated goals inside guardrails, should be designed and evaluated. We answer in two parts. First, we synthesize the Governed Autotelic Multi-Agent Product Organization (GAMPO) framework from a document-based qualitative evidence synthesis of 321 sources, integrating agency, agile, platform, and governance theory into a runnable specification. Second, we probe a prompt-layer instantiation of GAMPO on CHI-Bench, a long-horizon healthcare benchmark, across open and frontier models. The result is a boundary condition: governance benefit is gated by a model's spare capacity and is domain- and model-specific. On capacity-constrained open models the full procedure yields no reliable benefit, whereas a single "verify your writes" sentence doubles task success (pass@1 2/20 to 4/20). At the frontier the same scaffold lifts prior-authorization 24% to 40% but nets zero on another model, a gap traced to a stable recommendation-override disposition. A second result refines the first: replacing the generic procedure with an answer-blind, per-task definition-of-done, keyed only to the case's own policy and published standards, never the hidden key, raises prior-authorization to 84% under best-of-five self-consistency (68% single-attempt, confirmed by a held-out board) and utilization-management to 44%, while care-management meets a subjective content-quality wall. The contribution is a named, auditable framework and capability-gated evidence that governance should be sized to spare capacity, and that at the frontier a case-grounded specification beats a uniform procedure. Findings are exploratory: partial instantiation, small per-cell samples (n = 5-25), and single trials.