Thanks to the kindness of another member, I have received more information! I will be documenting this particular watch on my blog, as I have also done for some other oddballs in my collection (the Büren Calibre 82 and Junghans Mega 1) for others to learn as well.
First, it appears that this watch is much more rare than I anticipated. Perhaps only a few dozen were made by CvdK before he retired in 2009. The prototype appeared at BASEL 95 but did not go on sale until the next year, switching from a 2892 to a 2824 in the mean time. The originals had "hinged" strap attachment that caused issues (rattling I guess) and conventional lugs were adopted. CvdK appears to have some issues sourcing cases as well, so some examples have straight lugs instead of my scrolled/screwed lugs.
Technically this is a "Mk II" model, with the MK I being a smaller ladies model and the Mk III being a 7750 chronograph. According to one document, just 3 Mk I, 10-12 Mk II, and and 15 Mk III Satellite du Monde watches were produced, all around 2000. Mine is number 39, so it is perhaps a later example in this very small series!
At some point, CvdK offered highly decorated movements with guilloche by Jochen Benzinger as an extra-cost option. My watch has one such movement, and it is indeed elaborately decorated! I love his work, and this is an unexpected bonus! And the rotor features the old Klaauw logo not the new "sun".
Shortly before he retired, CvdK again offered this model. It was now known as the CK4 and included a date above 6:00 on the dial. They may have been produced in greater numbers, since I see a few more of these around the Internet. Or it could be that people just took more photos in 2008!
I was also provided with a copy of the (one page) manual. The "quick set" of the moon indication is quite complex and I never would have guessed how to do it, as it requires a "gentle tap" on the case! I will document this on my blog once I figure it out... But it does include the tidbit that the moon indicator makes one rotation around the dial every 24.84210526 hours, compared to the obvious 24 hours for the sun. I suppose this would technically be a synodic calendar?
Thanks again everyone!