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I ended up changing my scene to use the Tachyon renderer. I was able to control the resolution of my scene with the arguments to the tachyon scene creator as well as control where the camera was, where it looked at, and what the zoom level was. I was also able to enable antialiasing. All of these options reduced whitespace and increased resolution!

This worked because I did not have any parametric surfaces, so I was able to turn my Spheres, Parametric Curves, and Annulus into Tachyon objects quite easily.