One of the keys for me is to treat the interaction like a task, with a plan that you stick to, and to avoid being in the moment or thinking a lot about the big picture.

Then you can just do the simple (but not easy) work of softly explaining a difficult situation. Like an actor in a movie.

If you start to think about "if this goes to court I'll be ruined!" or "I can't believe I wasted 3 months of my life for these jerks" it becomes really difficult.