  We report muon spin rotation ($\mu$SR) and neutron diffraction on the
rare-earth based magnets (Mo$_{2/3}$RE$_{1/3}$)$_2$AlC, also predicted as
parent materials for 2D derivatives, where RE = Nd, Gd (only ($\mu$SR), 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 time
scale. 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 $m
= 6.5 \pm 0.5 \mu_B$, N\'eel temperature of $29 \pm 1$ K, and the magnetic
anisotropy between in and out of 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 if exfoliated
into 2D sheets.
