Hi Leo,
I did a small investigation today and verified that using your source .xml file, navTree webpart entries appear in the left and right 'Add Web Part' menus as you report. Second, I ran a simple search through the source and did not find any other examples where someone has used a file based webpart that could be added strictly on the right. I have opened an issue to one of our developers at LabKey and will try to keep you posted regarding what we find.
Thanks for the feedback,
Greg