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The homogeneous precession domain (HPD) of superfluid 3 He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling 𝑔𝑎⁢𝑁⁢𝑁 competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a nonstationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching 𝑔𝑎⁢𝑁⁢𝑁 ∼10−12  GeV−1 across a decade in axion mass.