I was thinking about something which I don't think I've seen mentioned here.
The reason that Coop is acting so differently and so much like Mr. C is not because he transferred realities. Also, I think that the Mc. C that we've seen throughout the series is different from the Mr. C that we hear a lot of stories about. Whenever Mr C is mentioned in the far past, the stuff with Diane, the meeting with Briggs. You get the impression that at least at first, he seems like regular coop. Diane mentions his evil smile when she was raped. Have we ever seen Mr. C smile in the entire series?
Look at the only other time we have seen Mr. C, in the S2 finale. He's totally different, rather manic, and very much an embodiment of BOB and Coop. He's practically none of this in S3. He is someone single-mindedly moving towards a goal, not letting anything stop him, nothing makes him happy, or sad. The best we can get out of him is anger.
I think that Mr. C was a lot more like the manic BOB until he did something. He made a Tulpa, he created Dougie. Now Dougie was a piece of crap, with a lot of issues, but he did seem to have emotions, show real fear, he was freaked out when he vanished in the red room. He felt more like a real person than Mr. C did.
All Mr. C has in Season 3 is his goal. EVERYTHING he does is either to keep himself out of the Red Room, to find Judy or to remove any obstacles in his path to either of the previous goals. The only other thing he cares about are basic impulses like food and sex, and he doesn't seem to get any joy out of them.
The other Tulpa we see is Diane's Tulpa, who is also very emotional. Compare her to the Diane in 17 and 18, who is muted by comparison. We don't get much time with her, but most scenes with real Diane she seems nearly as gone as Mr. C, she has her goal, but it's not as strong an impulse for her, so she loses herself completely in the new world.
It looks like when you make a Tulpa of someone, that person loses a bit of their soul for lack of a better term. They are the same person, but less so. They are less emotional, they are more single minded. In many ways the Tulpa becomes more of a real person than the original upon its creation.
So Richard/Coop has been changed, but he did it to himself. In creating Dougie again, he lost a lot of the better parts of himself, his warmth, his empathy for others. All he is left with is his need to save Laura, his very base good personality, his desire for sex and that's about it. It's not that he ISN'T Coop, he's just a lot less Coop.
That does add a lot of new meaning to the Dougie reunion scene though, it's not just Coop leaving a replacement behind. It's Coop sacrificing a huge part of himself for the Jones family. It's poignant, and it may be the last really warm thing we will ever see Coop do.