I don't know enough about projects to give you an authoritative answer to your question about which projects would best be consulted about the Leete family (btw my wife is a descendant of this family) but as no one else has answered I will go ahead and suggest that you might consider consulting the England Project for the parts of the lines listed back there, and perhaps the Puritan Great Migration project and the Connecticut project for the first few generations of Governor Leete's descendants in the Guilford & New Haven areas.
"The Family of Leet" book, if I recall correctly, was published in 1881. Some parts of the information, at least with respect to the descendants in the new world, has been augmented and in some respects superseded by a later work, which you might want to have a look at also:
Leete, Edward Lorenzo,. "The descendants of William Leete, one of the founders of Guilford, Conn., president of the Federation of Colonies and Governor of New Haven and Connecticut colonies." New Haven: Tuttle, Morehouse & Taylor, 1934
I have access to at least portions of both books, and if I can help you with any of the profiles you work on, let me know.