Due to their ubiquitous presence in spinning hard-drive technologies and growing potential as commercially viable memory bits, magnetic tunnel junctions (MTJs) continue to provide impetus for scientific study. The demand for smaller devices and efficient energy consumption mandates further investigation of their thermal properties and possible finite-size effects. We present a theoretical study of the magneto-Seebeck effect in MgO-based MTJs that employ both ferromagnetic (CoPt) and non-magnetic (Pt) spin-orbit coupled electrodes. Such material configurations enable us to investigate the Tunneling Magnetoresistance (TMR) and the Tunneling Anisotropic Magnetoresistance (TAMR) in conjunction with the magneto-Seebeck effect. We demonstrate that numerically-unstable transmission resonances, ordinarily described as hot-spots in the literature, more accurately resemble "walls" that weave through the Brillouin Zone. We discuss their physical relevance in modern day nanostructures, and argue that their selective removal (via filtering algorithms) provides a consistent and numerically-viable estimate of both the magnetoresistance and the magneto-Seebeck effect. Furthermore, we report that the magneto-Seebeck ratio of our TAMR structure exceeds that of the TMR structure for small barrier lengths, in contrast with the magnetoresistance, which behaves oppositely for all barrier lengths. We therefore conclude that exploiting spin-orbit coupling in MTJs with a single ferromagnetic contact can actually enhance certain magneto-transport anisotropies.