Despite its industrial relevance, the exploration of primary atomization within a transonic self-generating pulsatile three-stream injector has been minimal. Our prior experimental and computational work was centered around compressible axisymmetric (AS) models and incompressible 3-D models for the purpose of obtaining spectral content and preliminary droplet size distributions. Here, the emphasis shifts to compressible 3-D computational models involving a non-Newtonian slurry and a much more inclusive computational domain in order to further elucidate droplet size information. Effects of numerics, turbulence model, and geometric parameters are revisited. In addition, a surrogate measure for injector face erosion is introduced. Lastly, links are discovered between responses in Sauter mean diameter and trends in AS modeling metrics. As with prior air-water work and incompressible slurry simulations, higher gas inner flow rate reduced droplet size measurably. While the temporal mean droplet length scale was relatively insensitive to numerics, turbulence model, compressibility, and modeled domain size, droplet size temporal variability responded very strongly to some of these effects; compressibility dampened the droplet variability, while increased inner gas flow augmented variability, and the use of a more rigorous turbulence model showed a mixed effect. It was found that designs with less retraction (smaller pre-filming region) produced smaller droplets and allowed increased process throughputs. Newly discovered correlation equations are provided and followed similar trends as some from the earlier AS work. Interestingly, it was also shown that droplet size can be correlated with spectral information from prior companion AS studies.