Sounds like you're looking for something Carl Roger-esque to me. But your insurance company is right, meta-analysis does show that outcomes are similar no matter the orientation. However, what is more important than anything else, and it appears that you have this, is trust in the person and the process.

I have similar issues with the psychologist that I go to. She operates differently than I expected. This makes it difficult for me a lot of the time. I just try and tell myself to go with the flow and what needs to come out will, in time.