Inspired by Sir Ridley, I thought to myself, What if I projected the image of the Death Star into a proper sphere that had the correct volumes of the superlaser, the trench, and the cuts in the surface as the Death Star II?
Here is a broad test. It allows you to move the view slightly. At some point you start seeing the trick, but it could be a nice tool to get static different points of views (by reparing the image a little) or to get slight movement like Sir Ridley suggested.