Paper II of this series described the chemical and microstructural evolution of ferri-ilmenite solid solutions during high-T quench and short-term annealing. Here we explore consequences of these Fe–Ti ordering-induced microstructures and show how they provide an explanation for both self-reversed thermoremanent magnetization and room-T magnetic exchange bias. The dominant antiferromagnetic interactions between (001) cation layers cause the net magnetic moments of ferrimagnetic ordered phases to be opposed across chemical antiphase domain boundaries. Magnetic consequences of these interactions are explored in conceptual models of four stages of microstructure evolution, all having in common that A-ordered and B-anti-ordered domains achieve different sizes, with smaller domains having higher Fe-content, lesser Fe–Ti order, and slightly higher Curie T than larger domains. Stage 1 contains small Fe-rich domains and larger Ti-rich domains separated by volumes of the disordered antiferromagnetic phase. Magnetic linkages in this conceptual model pass through disordered host, but self-reversed TRM could occur. In stage 2, ordered domains begin to impinge, but some disorder remains, creating complex magnetic interactions. In stages 3 and 4, all disordered phase is eliminated, with progressive shrinkage of Fe-rich domains, and growth of Ti-rich domains. Ordered and anti-ordered phases meet at chemical antiphase and synphase boundaries. Strong coupling across abundant antiphase boundaries provides the probable configuration for self-reversed thermoremanent magnetization. Taking the self-reversed state into strong positive fields provides a probable mechanism for room-temperature magnetic exchange bias.