This would explain why some people recommend starting sentences with "I think..." etc. to reduce conflicts.
In a model-sharing mode that does not make much sense.

I think it can.

In a model-sharing mode that does not make much sense. Sentences "I think X" and "X" are equivalent.

You're on to something with analyzing the meaning of statements in different modes.

You can speak in model sharing mode with self awareness of the mode. So when I'm thinking about sharing my model, I'm aware that it's my model, and not yours.

So , "I think", "you think" maintains the awareness of which model one is speaking of, and an awareness of the situation you are in - two people with different models.

Earlier, I concluded that "I disagree" was better than "You're wrong" and "That's wrong". Maybe I'm seeing a principle emerge.

Discuss the topic in language that you could both agree on (that doesn't automatically conflict with the person you're talking to). We can both agree that "I disagree", but not that "You're wrong". With conscious of abstraction, and consciousness of our differing abstractions, we can jointly model our disagreement in a shared and consistent language.

That helps to "handle" the situation in terms of properly framing it as a clash of models, in terms that we can both agree on, but that's a joint "handling", coming to a common ground for discussion.

Though that likely changes our emotional reactions, that seems to me different than a direct attempt to handle your emotional state. It's primarily about coming up with an efficient language for our discussion.

I would guess that the general semantics crowd has analyzed discussions in similar terms but greater depth. What I'm saying here rings a lot of bells on readings from GS. Too bad I don't have concrete citations.