Metal hydrides are being seriously considered for advanced nuclear reactor or microreactor applications due to their solid physical state and high hydrogen density. Using hydrides for autonomous applications poses several research and development challenges, one of which relates to neutron upscattering in the thermal energy regime. These hydrides, including zirconium hydride and yttrium hydride, result in a positive temperature coefficient of reactivity for several advanced reactor designs. In this study, we consider one such design that exhibits positive feedback from metal hydrides and thoroughly investigate the neutronic aspects of the core. Temperature reactivity coefficients for four fuels and two hydride moderator configurations are studied, and the total temperature coefficients are found to be positive for all designs, showing that this issue cannot be resolved simply by material variations. Accordingly, five epi-thermal absorbers were evaluated to demonstrate the feasibility of the excess positive feedback suppression in the core instigating from neutron energy spectrum shift. Following which, two promising burnable poison candidates are selected to investigate further throughout the core discharge. Promising results are shown for this core design, which can be extended to other hydride-moderated remote special-purpose reactor designs.