I had some problems breaking the support structure from the inner ball, so I brought it into blender, separated the inner and outer balls into separate meshes, and separated the inner ball from its support.

I then hollowed the support.

The original support is still in the blender file along with the hollowed support and the inner and outer balls, all in different layers for easy mix and match or additional editing. Also, just in case someone wants to print the parts separately (and, like, cheat by dropping the inner one into the other one after it is half printed), I will include STL files for both the two balls together with the hollow support, and the two separate balls.

Print all the pieces together as meshball-hollow-support.

When it is done, crush the hollow support pole to remove it.

== OR ==

Print inner first and clean it up. Print outer, and when enough has printed to be taller than the inner piece, drop the inner piece in. (I haven't tried this with this model, but it has worked with others.)