  We study a parametrically forced nonlinear Schr\"odinger (PFNLS) equation,
driven by multiplicative translation-invariant noise. We show that a solitary
wave in the stochastic equation is orbitally stable on a timescale which is
exponential in the inverse square of the noise strength. We give explicit
expressions for the phase shift and fluctuations around the shifted wave which
are accurate to second order in the noise strength. This is done by developing
a new perspective on the phase-lag method introduced by Kr\"uger and Stannat.
Additionally, we show well-posedness of the equation in the fractional Bessel
space $H^{s}$ for any $s \in [0,\infty)$, demonstrating persistence of
regularity.
