Dynamical Dark Matter (DDM) is an alternative framework for dark-matter physics in which the dark sector comprises a vast ensemble of particle species whose Standard-Model decay widths are balanced against their cosmological abundances. Previous studies of this framework have focused on a particular class of DDM ensembles in which the density of dark states scales roughly as a polynomial of the mass. In this talk, by contrast, we discuss the properties of DDM ensembles in which the density of dark states grows {\it exponentially}\/ with mass, as appropriate if the dark-sector constituents are the ``hadronic'' resonances associated with the confining phase of a strongly-coupled dark sector. We find that rather generic cosmological constraints introduce non-trivial correlations between the mass scales, lifetimes, and abundance distributions associated with these DDM ensembles. For example, we find that such DDM ensembles can exhibit energy scales ranging from the GeV scale all the way to the Planck scale, but that the total present-day cosmological abundance of the dark sector must be spread across an increasing number of different states in the ensemble as these energy scales are dialed from the Planck scale down to the GeV scale. This talk reports on work originally presented in Ref.~[1].