The moment analysis method (MA) has been tested for the case of 2S --> 2P ([core]ns1 --> [core]np1) transitions of alkali metal atoms (M) doped into cryogenic rare gas (Rg) matrices using theoretically validated simulations. Theoretical/computational M/Rg system models are constructed with precisely defined parameters that closely mimic known M/Rg systems. Monte Carlo (MC) techniques are then employed to generate simulated absorption and magnetic circular dichroism (MCD) spectra of the 2S --> 2P M/Rg transition to which the MA method can be applied with the goal of seeing how effective the MA method is in re-extracting the M/Rg system parameters from these known simulated systems. The MA method is summarized in general, and an assessment is made of the use of the MA method in the rigid shift approximation typically used to evaluate M/Rg systems. The MC-MCD simulation technique is summarized, and validating evidence is presented. The simulation results and the assumptions used in applying MA to M/Rg systems are evaluated. The simulation results on Na/Ar demonstrate that the MA method does successfully re-extract the 2P spin-orbit coupling constant and Landé g-factor values initially used to build the simulations. However, assigning physical significance to the cubic and noncubic Jahn-Teller (JT) vibrational mode parameters in cryogenic M/Rg systems is not supported.