I think most of that is right. But I don't really see Carr as a pocket passer or a bootleg guy. He's okay at both, but his super power is the play action passing game and particularly the deep ball off of it. If you sit him in the pocket as a drop back passer all too often he ends up holding the ball too long and then throwing it away because he lacks the pocket mobility to buy time for off schedule throws. I think he's best used when you limit his options, limit the time he has to think, and just make him throw quick off of play action. That's what KK did with him in the first two games and it worked well. It seemed to not work well when he tried to get Carr to sit in the pocket.
Which is going to be interesting because Moore likes to vary tempo on offense and Carr seems a difficult fit for that kind of offense. That said, Moore is the type that will adjust to the players he has so we will likely see less tempo than Moore would like.