You have every right to assess a poor personality fit after a phone call and an in-person session. I think you need to decide if it is something you want (or must) work through, or if you'd like to find someone you click better with from the start. Therapy is hard enough without having to overcome personality conflicts. I know that you also came out of an emotional therapy relationship a few months ago, which may be coloring your perception.

For what it's worth, I interviewed and consulted with quite a few therapists after termination with my long term ex-therapist, and after being dissatisfied with everyone I met, I chose to go with a really cold EMDR/CBT therapist to process therapy trauma only. I think it came down to what I needed at the time. Perhaps looking at what, specifically, would make a 'good enough' therapist for you and then trying to find it might help? If you're stuck with the one you have, it might help to assess her skills and personality, and identify some area she could help with. It doesn't have to be intimate depth-work.

I wouldn't have thought much about the tissue placement. Seems to be more of a red herring for the real issue.