Thanks for responding so quickly.

I believe that I've understood everything you said except the directions to do a RemoveFromGroup first. 

Is this a programmer's suggestion, for tidiness sake, pointing out that I need to go through and clean up the old group's polygon assignments before adding the new ones or is this a Poser Python expert's statement because of something in the operation of Poser Python?

Almost all of my experiments with this have worked without doing the RemoveFromGroup.  I'm still chasing a weirdness with reloading a pz3 file.