Mesoscopic hysteresis models are based on a simplified description of the micromagnetic theory in order to simulate magnetization processes on the magnetic domain space scale. Hence, these models are situated between the micromagnetic and macroscopic models. In the presented mesoscopic description, the local magnetization is assumed to be aligned with either the cubic anisotropy axes or with the applied field. In this framework, the magnetization dynamics result from a constrained minimization of the Gibbs free energy. The numerical solution of this constrained minimization problem is highly time consuming. This paper presents a remapping of the model variables, which transforms the constrained minimization problem to an unconstrained problem and consequently results in a speed up and stabilization of the numerical scheme. Moreover, a model parameter analysis is carried out to further optimize the computational burden of the presented unconstrained procedure.