Primary atomization within a transonic self-generating pulsatile three-stream injector has important industrial relevance; however, very few studies have explored the intricacies of these dynamic flows. Prior computational work used compressible axisymmetric (AS) models and incompressible 3D models for the purpose of obtaining spectral content and preliminary droplet size distributions, which was validated with experiments. The emphasis of the work herein shifts to compressible 3D computational models for a non-Newtonian slurry and a more inclusive computational domain to further elucidate droplet size information. Effects of numerics, turbulence model, and geometric parameters are investigated. 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 computational domain size, droplet size temporal variability responded very strongly to some of these effects. It was found that injector designs with less retraction (smaller prefilming region) produced smaller droplets and allowed increased process throughputs. Newly discovered correlation equations are provided and followed similar trends to AS work. Interestingly, it was also shown that droplet size can be correlated with spectral information from companion AS studies.