We perform a parametric study of highly oblique solitary and periodic nonlinear stationary slow magnetoacoustic waves in the model of McKenzie and Doyle, and Stasiewicz, taking plasma pressure anisotropy into account. The model was proposed for the interpretation of linear magnetic holes, where there is almost no variation in direction of the ambient magnetic field direction. In particular, we focus on magnetic structures in high-β (ratio of kinetic to magnetic pressures) plasmas. We find that gas pressure anisotropy is crucial for the existence of solitary structures in this model for the parameter regime considered. Pressure anisotropy leads to the existence of field enhancing bright solitary structures and field depleting dark solitary structures. To explain the parametric range of the existence of solitary and periodic wave solutions of the model, a pseudo-(Sagdeev) potential is used. We obtain an analytic form for this potential in the case of low Alfvén mach waves. We find that the potential method accurately predicts the parametric range of the existence of solitary waves as calculated by direct numerical simulations.