Doe, thanks for this helpful comparison of 3 NH orgs, & I find that your 3 strategies are, in fact, what these people use.
The addition of Partnership/Trust/"Want-to" was also my thought, & this, ime, is the difference between the teachers:
Parelli emphasizes, "Anyone can make his horse do something, but can you cause your horse to want to?", "Your horse doesn't care how much you know till he knows how much you care.", "Can you be interesting/provocative to your horse?" etc.
Anderson, on the other hand, makes no such statements that I can recall (if my memory isn't serving me, I'd love some quotes from him!) & I was a "No Worries Club" member for a year. Anderson says, "Get the job done!" This is not to start a fan war, but to point out this all-important difference between any two riders who do have a difference.
La Cense I'm unfamiliar with, so can't comment.
The horse is only happy with a real horseman, who by definition has gone beyond making the horse do tasks, to being a fun & capable leader for his horse.