This study analyzed an yttrium hydride (YH2) moderated supercritical carbon dioxide cooled reactor loaded with pin-type, beryllium oxide diluted oxide fuel elements to reduce the critical enrichment. The impact of the YH2 on the coolant void reactivity was studied along with a moderator zoning scheme to flatten the radial power distribution. The YH2 was added as hexagonal moderating rods at the center of the fuel assemblies. The core was modeled using the continuous-energy Reactor Monte Carlo code (RMC) with the on-the-fly cross sections treatment. The results showed that the YH2 moderator increased the thermal fission and reduced the critical enrichment of the core with the same diluent volume fraction by more than 30%. The YH2 moderator significantly softened the neutron energy spectrum and reduced the neutron leakage upon core voiding, resulting in both a weaker positive spectral reactivity feedback and a weaker negative leakage reactivity feedback during core depressurization. For an UO2-loaded core, the YH2 gave a lower negative coolant void reactivity, while for a mixed oxide fuel (MOX)-loaded core with diluent volume fractions smaller than 35%, the spectral feedback was more important and the YH2 strongly reduced the positive coolant void reactivity to less than $1. Arranging the YH2 in the peripheral assemblies reduced the radial power peaking factor to 1.319. The study shows that the YH2 moderator can reduce the critical enrichment, make the core less sensitive to voiding, and can flatten the radial power distribution of a single-enrichment core through moderator zoning.