  We explore a missing-partner model based on the minimal SU(5) gauge group
with $\bf{75}$, $\bf{50}$ and $\bf{\overline{50}}$ Higgs representations,
assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking
parameters are universal at some high scale $M_{\rm in}$ above the GUT scale
$M_{\rm GUT}$. We identify regions of parameter space that are consistent with
the cosmological dark matter density, the measured Higgs mass and the
experimental lower limit on $\tau(p \to K^+ \nu)$. These constraints can be
satisfied simultaneously along stop coannihilation strips in the super-GUT
CMSSM with $\tan \beta \sim 3.5 - 5$ where the input gaugino mass $m_{1/2} \sim
15 - 25$~TeV, corresponding after strong renormalization by the large GUT Higgs
representations between $M_{\rm in}$ and $M_{\rm GUT}$ to $m_{\rm LSP},
m_{\tilde t_1} \sim 2.5 - 5$~TeV and $m_{\tilde g} \sim 13 - 20$~TeV, with the
light-flavor squarks significantly heavier. We find that $\tau(p \to K^+ \nu)
\lesssim 3 \times 10^{34}$~yrs throughout the allowed range of parameter space,
within the range of the next generation of searches with the JUNO, DUNE and
Hyper-Kamiokande experiments.
