  Supersymmetric $SO(10)$ models with Yukawa coupling matrices involving only a
$10_H$ and a $\overline{126}_H$ of Higgs fields can lead to a predictive and
consistent scenario for fermion masses and mixings, including the neutrino
sector. However, when coupled minimally to a symmetry breaking sector that
includes a $210_H$ and a $126_H$, these models lead either to an unacceptably
small neutrino mass scale, or to non-perturbative values of the gauge
couplings. Here we show that with the addition of a $54_H$ to the symmetry
breaking sector, the successful predictions of these models for fermion masses
and mixings can be maintained. The $54_H$ enables a reduction of the $B-L$
symmetry breaking scale to an intermediate value of order $10^{12}$ GeV,
consistent with the observed neutrino mass spectrum, while preserving
perturbative gauge coupling unification. We obtain an excellent fit to all
fermion masses and mixings in this framework. We analyze carefully the
prediction of the model for CP violation in neutrino oscillations. Consistency
with proton lifetime, however, requires a mini-split SUSY spectrum with the
squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale
gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation,
which would predict the partial lifetime for the decay $p \rightarrow
\overline{\nu} K^+$ to be an order of magnitude above the current experimental
limit.
