  Next-generation ultra-high-energy (UHE) neutrino telescopes, presently under
planning, will have the potential to probe the decay of heavy dark matter (DM)
into UHE neutrinos, with energies in excess of $10^7$~GeV. Yet, this potential
may be deteriorated by the presence of an unknown background of UHE neutrinos,
cosmogenic or from astrophysical sources, not of DM origin and seemingly large
enough to obscure the DM signature. We show that leveraging the angular and
energy distributions of detected events safeguards future searches for DM decay
against such backgrounds. We focus on the radio-detection of UHE neutrinos in
the planned IceCube-Gen2 neutrino telescope, which we model in state-of-the-art
detail. We report promising prospects for the discovery potential of DM decay
into UHE neutrinos, the measurement of DM mass and lifetime, and limits on the
DM lifetime, despite the presence of a large background, without prior
knowledge of its size and shape.
