This release forms part of the Computational Observerhood Labs of Mirror Programme, Volume I: Observerhood. Lab III tests whether reliability variables become viability-relevant only when they are coupled to actionable and cost-sensitive repair. It follows Mirror Observerhood Lab I, which showed that scalar self-model reliability can help under false self-location, and Mirror Observerhood Lab II, which showed that decomposed reliability alone is insufficient. Across 4,800 deterministic grid-world episodes, four architectures are compared: a no-reliability baseline, a passive reliability agent, a threshold-repair agent and a cost-sensitive Mirror agent. The cost-sensitive Mirror agent outperforms the strongest non-Mirror baseline under false self-location, map corruption and mixed low-cost perturbation, but underperforms where repair is unnecessary, poorly matched or too expensive. The central finding is that reliability tracking is not enough. Reliability becomes observer-relevant only when it changes action, repair or commitment in a way that improves viability after cost. The release includes a standalone paper and a reproducibility package containing the Python implementation, fixed-seed outputs, summary data, cost-sensitive advantage data, figures, requirements, citation metadata and licences.