In this work, a solid-phase thermodynamic model is coupled with the Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equations of state (EoS) to model the solid-liquid-gas equilibrium (SLGE) of binary methane (CH4) mixtures with normal alkanes (n-alkanes). The mixtures considered include n-alkanes from n-C6H14 up to n-C36H74. The predictive capabilities of each combined model are validated against available experimental data and vary substantially as the asymmetry of the binary mixture, with respect to the size of the molecules involved, increases. Several aspects of the models, such as the use of binary interaction parameters (BIPs) fitted to experimental vapor (or gas)-liquid equilibrium (VLE/GLE) data and the importance of specific terms of the solid-phase model, are studied to showcase their effect on the accuracy of the calculations. In this way, modifications on the basic combined models are applied. A specific volume translation strategy is adopted for the cubic EoS, in order to describe more accurately the liquid molar volume pressure dependency in the Poynting correction of the solid-phase fugacity. This dependency becomes particularly important for highly asymmetric mixtures, in which SLGE is exhibited at very high pressures. A correlation of the BIPs with the carbon number of n-alkanes is proposed for each fluid-phase EoS, which can be used as a practical alternative to fitting k(ij) parameters for other similar mixtures at a relevant range of conditions. Finally, by combining two previously published approaches for calculating the solid-phase fugacity, a new solid-phase model is proposed and calculations are presented in combination with the PR and the PCSAFT EoS. Every combined model studied in this work retains a predictive nature, except for the newly proposed one, which requires a direct fit to the binary SLGE data. Calculations using the predictive models proposed in this work are in very good agreement with experimental measurements even at high pressures for most mixtures, while the proposed approach for the solid phase shows excellent accuracy in correlating the experimental data. Global phase diagrams are calculated with the adopted and proposed models for specific mixtures to showcase their ability to accurately reproduce the global phase behavior in a wide range of conditions.