At this point it's probably only beneficial to follow the trail of "experts" as they challenge each other with the mystery.
Another curator noticed a strange coincidence. My illustration is labeled "XXIV". A different illustration of the same three models is also labeled "XXIV" in Johannes Kepler's 1609 book "Astronomia Nova".
The illustration in Kepler's book:
For Kepler's book the illustration was produced from a woodcut. My illustration was produced from a copper-plate engraving and then colored by hand.