You might want to look into a Medicare Advantage Plan. That might get you access to psychiatrists who are not part of a public clinic. Pdocs at those places tend to be just passing through. I know from personal experience.

I'm facing the decision, myself, right now, of whether to stay where I'm at, which is a public facility and I've had 3 different pdocs . . . . or get me an Advantage plan, which would hook me up with some pdocs in a group affiliated with the Advantage plan, where they stay put for years and years.

Also, like you, I was on a benzo, which I had to give up. I'm not sure how the pdocs at the Advantage Plans would feel about letting me have a sleeping pill. (I was on Restoril, and had to give that up.)

It can be real tedious trying to study all the options out there. Then you don't really know what any new doctor will do, until you have become his/her patient.