I don't think I'd like to do solution-focused therapy as a treatment for trauma. That just seems counterintuitive to me.

If you feel like you need to talk about your past and get it out of you, then it seems to me that seeing a therapist who works with a modality that specifically excludes the past would be a bad idea. She has already told you that she will be working in a way that does not place value on the past, so you can expect her to redirect you should you try to steer the discussion to your past experiences. I think that would probably be very upsetting and potentially traumatic.