Thank you for the write-up!
So if I was to break up the concepts into an D&D style
Neutral: X-Men, focused on mutant-threats mainly
Chaotic: Uncanny X-Men, outlaws that try to be superheroes
Lawful: X-Factor, from the description it's a government sanctioned team
With Exceptional, NYX and X-Force mostly keeping to themselves.
Completely guessing, but getting the feeling X-Factor and X-Men might clash.