>I notice the colors also become more saturated after postprocessing in your examples, is this after it finds the closest color in the palette or the result of the postprocess?

It's the result of the Blender compositor postprocessing, just keep in mind it falls apart once you go low enough in resolution (it's an image space thing after all), so I'm not sure if that helps your case.

EDIT: Also, your project is very cool!