The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedal et al. (Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.