Your theory was a very interesting read, and it does bring up many interesting points. Obito's kamui is, as Minato observes, a space/time technique that goes beyond his and Tobirama's. I too believe that he did not mean it was "better" as a jutsu perse, but more complex of a jutsu overall. Let us contemplate the instances that you brought up in your theory.
Obito surviving amaterasu
Obito saving Sasuke from jinton
Obito potentially trying to save Sasuke from being beheaded
The first instance showed Obito being struck with the jutsu, suffering from it, and disappearing into the shadows, only to emerge afterwards visibly unharmed. His clothes were not even charred, which is suspicious, seeing as amaterasu burned through two layers to get to Karin's back (though it did not burn through the samurai armor.) I have no explanation for that as of yet, so I will just leave it at that.
However, the next two instances may be explained without a time altering reason. I agree with you when you say that kamui puts the user in a dimension totally different from the Naruto world and Obito's world. Obito can be seen visibly, but upon contact any of his body parts and equipment is instantaneously in the other dimension. Equipment is the key word of my argument, because that means anything that he touches and chooses to pass his intangibility to will also be in a similar state as him. I believe that he could have entered the jinton, touched Sasuke, and made him intangible as well to survive the technique, the same is if he was holding a kunai. The same reasoning can be applied to his warping to save Sasuke from Danzo, however in that case there were two options that could be taken. Obito could have saved Sasuke via the same touch induced intangibility that he may have used at the kage summit, or he could have simply attacked Danzo directly.
With the above said, I am not entirely against the theory that kamui possesses latent time controlling abilities. Time space techniques are one's that receive the least universal explanations, due to their rarity and their (supposed) easily analyzed results. I would appreciate more concrete examples before I make my final decision.
