Oh, I'd never suggest that Kirk - Pine or Shatner - isn't cunning and manipulative, particularly where women are concerned. He's not cold or particularly calculating, though. And I think the writers of ST took the Kobyashi Maru story in the only direction they could by making it such a clear cheat that it's hard to argue that Kirk didn't know that it would be recognized immediately as such. What he clearly didn't expect was to miss out on the big galactic crisis because of being suspended.
I think you're missing the point, a little, on the dart thing - I didn't say that Mitchell wasn't portrayed as brave or incapable of being loyal. But since he never actually was injured - in the sense that this is fiction where everything is either invented or not sheerly at the need of the author - what's most important in IMAO is why we get to hear this incident referred to. There are two answers, I think - one is to make Kirk suffer a little more for the benefit of the audience, and the other is to show Mitchell once again pulling someone's strings.
In terms of how action and history reveal the characters in stories, they have only those characteristics given to them by the writer of the story (behavioral nuance being the province of the actor and perhaps the director). They don't have light and dark sides on their own, they do nothing for the sake of anything other than the script itself.
Mitchell's not "becoming a manipulator" - the earliest description of his behavior (the lab assistant story) is of his being a manipulator. The only thing he's becoming, in the story, is unstoppable.