The key insight in this work consists of introducing a dampening factor Φ(µ (3) , µ (4) ) that is applied to the bare third order cumulant correction, where Φ is taken to be an explicit function of the skew and excess kurtosis, measures of the non-Gaussian nature of the energy gap fluctuations. We have rationalized the functional form of this correction factor by noting that the third order cumulant term improves the spectral lineshape in the short timescale, but exhibits divergences at longer timescales. These divergences would be cancelled by higher order cumulant contributions that have to be neglected in any practical application to condensed phase systems. Thus the factor Φ approximately accounts for the collective dampening contribution to the lineshape of higher order cumulants.