  Based on the stochastic superspace mechanism for softly breaking
supersymmetry, we present improved sparticle spectra computations for the
minimal model and examine extensions through R-parity violation and the type-I
seesaw mechanism that incorporate non-zero neutrino masses for more realistic
models. Performing the calculations to two-loop accuracy, we observe a global
decrease in predicted sparticle masses. However this does not affect the
generic features of the minimal model outlined in our earlier work, including
the characteristic light stop mass. We find stop decay channels accessible at
the LHC which can be used in combination with our predicted range for the stop
mixing angle to falsify the minimal model with stochastic supersymmetry. We
then introduce neutrino masses and mixings consistent with experiment by
including purely trilinear R-parity violating superpotential terms, resulting
in a viable stochastic superspace model absent a dark matter candidate. An
alternative method for generating neutrino masses, namely the type-I seesaw
mechanism, is found only to be viable when the neutrino Yukawa coupling is
small relative to the top Yukawa and the cut-off scale is large.
