OK, while searching for riddles for a certain riddle game ( [img]smilies/biggrin.gif[/img] ) I came across yet another interesting snippet. In Norse mythology, creation is divided into 9 Worlds.
Since we know one of Tolkien's major influences was Beowulf and other tales from Norse mythology, (The name "Gimli" is the Hall of the Gods, or Paradise) I'm even more inclined to believe that he was making deliberate choices when it came to those pesky numbers.
If you'd like to learn more about the Nine Worlds, and perhaps find other references that Tolkien "borrowed", click here:
The Nine Worlds