  Through analysis of variable temperature neutron powder diffraction data, we
present solutions for the magnetic structures of SrMn$_7$O$_{12}$,
CdMn$_7$O$_{12}$, and PbMn$_7$O$_{12}$ in all long-range ordered phases. The
three compounds were found to have magnetic structures analogous to that
reported for CaMn$_7$O$_{12}$. They all feature a higher temperature lock-in
phase with \emph{commensurate} magneto-orbital coupling, and a delocked,
multi-\textbf{k} magnetic ground state where \emph{incommensurate}
magneto-orbital coupling gives rise to a constant-moment magnetic helix with
modulated spin helicity. CdMn$_7$O$_{12}$ represents a special case in which
the orbital modulation is commensurate with the crystal lattice and involves
stacking of fully and partially polarized orbital states. Our results provide a
robust confirmation of the phenomenological model for magneto-orbital coupling
previously presented for CaMn$_7$O$_{12}$. Furthermore, we show that the model
is universal to the $A^{2+}$ quadruple perovskite manganites synthesised to
date, and that it is tunable by selection of the $A$-site ionic radius.
