  The recent detection of the live isotopes $^{60}{\rm Fe}$ and $^{244}{\rm
Pu}$ in deep ocean sediments dating back to the past 3-4 Myr poses a serious
challenge to the identification of their production site(s). While $^{60}{\rm
Fe}$ is usually attributed to standard core-collapse supernovae, actinides are
r-process nucleosynthesis yields, which are believed to be synthesized in rare
events, such as special classes of supernovae or binary mergers involving at
least one neutron star. Previous works concluded that a single binary neutron
star merger cannot explain the observed isotopic ratio. In this work, we
consider a set of numerical simulations of binary neutron star mergers
producing long-lived massive remnants expelling both dynamical and spiral-wave
wind ejecta. The latter, due to a stronger neutrino irradiation, also produce
iron-group elements. Assuming that large-scale mixing is inefficient before the
fading of the kilonova remnant and that the spiral-wave wind is sustained over
a 100-200 ms timescale, the ejecta emitted at mid-high latitudes provide a
$^{244}{\rm Pu}$ over $^{60}{\rm Fe}$ ratio compatible with observations. The
merger could have happened 80-150 pc away from the Earth and between 3.5 and
4.5 Myr ago. We also compute expected isotopic ratios for eight other live
radioactive nuclides showing that the proposed binary neutron star merger
scenario is distinguishable from other scenarios proposed in the literature.
