  In previous work, we presented a statistical scan over the soft supersymmetry
breaking parameters of the minimal SUSY $B-L$ model. For specificity of
calculation, unification of the gauge parameters was enforced by allowing the
two ${\mathbb Z}_{3}\times {\mathbb Z}_{3}$ Wilson lines to have mass scales
separated by approximately an order of magnitude. This introduced an additional
"left-right" sector below the unification scale. In this paper, for three
important reasons, we modify our previous analysis by demanding that the mass
scales of the two Wilson lines be simultaneous and equal to an "average
unification" mass $\left<M_{U}\right>$. The present analysis is 1) more
"natural" than the previous calculations, which were only valid in a very
specific region of the Calabi-Yau moduli space, 2) the theory is conceptually
simpler in that the left-right sector has been removed and 3) in the present
analysis the lack of gauge unification is due to threshold
effects--particularly heavy string thresholds, which we calculate statistically
in detail. As in our previous work, the theory is renormalization group evolved
from $\left<M_{U}\right>$ to the electroweak scale--being subjected,
sequentially, to the requirement of radiative $B-L$ and electroweak symmetry
breaking, the present experimental lower bounds on the $B-L$ vector boson and
sparticle masses, as well as the lightest neutral Higgs mass of $\sim$125 GeV.
The subspace of soft supersymmetry breaking masses that satisfies all such
constraints is presented and shown to be substantial.
