  Direct searches for Dark Matter (DM) are continuously improving, probing down
to lower and lower DM-nucleon interaction cross sections. For
strongly-interacting massive particle (SIMP) Dark Matter, however, the
accessible cross section is bounded from above due to the stopping effect of
the atmosphere, Earth and detector shielding. We present a careful calculation
of the SIMP signal rate, focusing on super-heavy DM ($m_\chi \gtrsim 10^5
\,\,\mathrm{GeV}$) for which the standard nuclear-stopping formalism is
applicable, and provide code for implementing this calculation numerically.
With recent results from the low-threshold CRESST 2017 surface run, we improve
the maximum cross section reach of direct detection searches by a factor of
around 5000, for DM masses up to $10^8 \,\,\mathrm{GeV}$. A reanalysis of the
longer-exposure, sub-surface CDMS-I results (published in 2002) improves the
previous cross section reach by two orders of magnitude, for masses up to
$10^{15} \,\,\mathrm{GeV}$. Along with complementary constraints from SIMP
capture and annihilation in the Earth and Sun, these improved limits from
direct nuclear scattering searches close a number of windows in the SIMP
parameter space in the mass range $10^6$ GeV to $10^{13}$ GeV, of particular
interest for heavy DM produced gravitationally at the end of inflation.
