Not sure if you will be able to use this technique inside the cage, but...
You can smooth something to a near perfect sphere using a circle slightly smaller than the diameter of the sphere. A circle intersects with a (larger) sphere all around the circle's circumference, meaning that if the circle is moved around on the surface of the sphere, it should abrade all the protrusions.
Saw it on mythbusters when they were trying to polish turds.
ETA: if you really want a ball in a cage ... aren't you married already?
