The preceding paper in this series [Mantouka, Dogan, White, and Leighton, J. Acoust. Soc. Am. 140, 274-282 (2016)] presented a nonlinear model for acoustic propagation in gassy marine sediments, the baseline for which was established by Leighton [Geo. Res. Lett. 34, L17607 (2007)]. The current paper aims further advancement on those two studies by demonstrating the particular effects of the sediment rheology, the dispersion and dissipation of the first compressional wave, and the higher order re-scattering from other bubbles. Sediment rheology is included through the sediment porosity and the definition of the contact interfaces of bubbles with the solid grains and the pore water. The intrinsic attenuation and the dispersion of the compressional wave are incorporated using the effective fluid density model [Williams, J. Acoust. Soc. Am. 110, 2276-2281 (2001)] for the far field (fully water-saturated sediment). The multiple scattering from other bubbles is included using the method of Kargl [J. Acoust. Soc. Am. 11, 168-173 (2002)]. The overall nonlinear formulation is then reduced to the linear limit in order to compare with the linear theory of Anderson and Hampton [J. Acoust. Soc. Am. 67, 1890-1903 (1980)], and the results for the damping coefficients, the sound speed, and the attenuation are presented.