Brian, You're doing a good detailed search! You haven't found one that will work yet, but keep going
Often insurance companies only cover certain types of therapy and therapists. To get what you want you could find someone you could pay on your own; leaving the insurance company out of the process can be very relieving, empowering, and it opens up more therapists from which to choose.
I found my therapist by contacting a psychoanalytic institiute in a large city near me and asking for someone in my community. That worked well for me, so maybe it's something you might consider doing. Here's a link to a site that helped me
psychoanalytic training institutes . My therapist has been a therapist for 20 years and is currently a candidate (student) at the institute. She's great and I'm so glad I found her.
Keep going Brian! I admire all the work you're putting into your search. It can be discouraging at times, but that will all fall away when you get throught the search process and find someone.