We report muon spin rotation (μSR) and neutron diffraction on the rare-earth-based magnets (Mo2/3RE1/3)2AlC, also predicted as parent materials for two-dimensional (2D) derivatives, where the rare earth (RE) = Nd, Gd (only μSR), Tb, Dy, Ho, and Er. By crossing information between the two techniques, we determine the magnetic moment (m), structure, and dynamic properties of all compounds. We find that only for RE = Nd and Gd the moments are frozen on a microsecond timescale. Out of these two, the most promising compound for a potential 2D high m magnet is the Gd variant, since the parent crystals are pristine with m=6.5±0.5μB, Néel temperature of 29±1K, and the magnetic anisotropy between out-of- and in-plane coupling is smaller than 10-8. This result suggests that magnetic ordering in the Gd variant is dominated by in-plane magnetic interactions and should therefore remain stable when exfoliated into 2D sheets.