Have you ever tried to solve a problem by having a written dialog with yourself?

No, but in the middle of the night I ask my brain to remember whatever is bothering me. Like the name of a celebrity or whatever. It works on its own every time.

Yes. It allowed me to see all that was going on at the same time in the context of the situation, things I hadn’t realized until then. Very helpful!

My brain works better when not overtaxing it like this when stuck. I can sort things in my mind without the need for paper. If I am still stuck on solutions, I let it marinate.
I sleep on it or take a walk to clear my mind. The solution comes after the clearing.

Never.

The closest I’ve come to that is writing a pros and cons list. If I’m trying to think of a name of a person or movie or something, I mentally go through the alphabet. That usually leads to one or two letters seeming right, and I concentrate on them until I come up with it. Almost always works.