  Alpha and cluster decays are analyzed for heavy nuclei located above
$^{208}$Pb on the chart of nuclides: $^{216-220}$Rn and $^{220-224}$Ra, that
are also candidates for observing the $2 \alpha$ decay mode. A microscopic
theoretical approach based on relativistic Energy Density Functionals (EDF), is
used to compute axially-symmetric deformation energy surfaces as functions of
quadrupole, octupole and hexadecupole collective coordinates. Dynamical
least-action paths for specific decay modes are calculated on the corresponding
potential energy surfaces. The effective collective inertia is determined using
the perturbative cranking approximation, and zero-point and rotational energy
corrections are included in the model. The predicted half-lives for
$\alpha$-decay are within one order of magnitude of the experimental values. In
the case of single $\alpha$ emission, the nuclei considered in the present
study exhibit least-action paths that differ significantly up to the scission
point. The differences in alpha-decay lifetimes are not only driven by Q
values, but also by variances of the least-action paths prior to scission. In
contrast, the $2 \alpha$ decay mode presents very similar paths from
equilibrium to scission, and the differences in lifetimes are mainly driven by
the corresponding Q values. The predicted $^{14}$C cluster decay half-lives are
within three orders of magnitudes of the empirical values, and point to a much
more complex pattern compared to the alpha-decay mode.
