The Dali left the Jedi after the Great Schism, in what is known as the Slightly Smaller Schism. They focus more on humour and unusual ways of looking at the universe (say, through a small piece of fairy cake), and its application to the Force. Also known as the Daft Side, or the Mojo Side. Talk to RJM for more info
As for your neutrals, I think they were probably founded around the time of the Exar Kun war, personally.