The crystal-melt equilibria in complex 15-component-simulated high-level waste (HLW) glass melts are modeled based on quasicrystalline concepts that are discussed in Part I. A pseudobinary phase diagram between a transition metal ferrite spinel (an incongruent melt product of a transition metal iron-rich acmite) and nepheline is defined based on calculation of the quasicrystalline melt precursors calculated by a freezing point depression approach. The pseudobinary lies within the Al2O3-Fe2O3-Na2O-SiO2 quaternary system that defines the crystallization of basalt glass melts. The modeling provides the partitioning of species between the melt and the primary liquidus phases. The medium-range order of the melt and the melt-crystal exchange equilibria are defined based on a constrained mathematical treatment that considers the crystallochemical coordination of the elemental species in acmite and nepheline. The liquidus phases that form are shown to be governed by the melt polymerization (Part II) and the thermodynamic octahedral site preference energies (Part I). The liquidus model developed based on these concepts has been used to prevent unwanted crystallization in the world's largest HLW melter for the past 4 years while allowing > 10 wt% higher waste loadings to be processed.