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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 $2 α$ 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 $α$-decay are within one order of magnitude of the experimental values. In the case of single $α$ 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 $2 α$ 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.