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The proposed designs of many auxiliary long-lived particle (LLP) detectors at the LHC call for the instrumentation of a large surface area inside the detector volume, in order to reliably reconstruct tracks and LLP decay vertices. Taking the CODEX-b detector as an example, we provide a proof-of-concept optimization analysis that demonstrates the required instrumented surface area can be substantially reduced for many LLP models, while only marginally affecting the LLP signal efficiency. This optimization permits a significant reduction in cost and installation time, and may also inform the installation order for modular detector elements. We derive a branch-and-bound based optimization algorithm that permits highly computationally efficient determination of optimal detector configurations, subject to any specified LLP vertex and track reconstruction requirements. We outline the features of a newly-developed generalized simulation framework, for the computation of LLP signal efficiencies across a range of LLP models and detector geometries.