Z-fighting/clipping issue with plotting objects on a globe (sphere)

I am starting work on a project where objects will be plotted on the earth. I've put together a quick test and found that when i position objects around a sphere, I have some clipping problems with the polygons of these objects. I put together an example to show what I'm talking about:

You can click to change from plotting planes to cubes. I've actually offset the planes a bit away from the radius of the sphere, but the clipping problem is still pretty severe. I once encountered something similar in an OpenGL project and it turned out to be z-fighting and after adjusting the near clip and far clip distance on my projection matrix, it was fine. I suspect something like this might be the cause of my problem, but I don't really understand the inner workings of the Papervision3D transformation pipeline.

Does anyone know how to get around this? Any tips? Thanks for any help.

-Aaron