Hi Calilady,
I have a couple of thoughts about your situation, which you may or may not like but this is what I think, being very avoidant myself.
First, it seems to me that by terminating like this (spontaneously, due to an argument) is itself an avoidant behaviour. You got close to something, expressed it in some way and she didn't respond perfectly and then you probably felt too vulnerable to tolerate it further (I'm partly fantasising here, right) and then you ran away. I have been in this kind of stalemate situation with my T (who is actually excellent) many times. I have sat there saying that I have no idea how we go on from this situation. I have ran out from the room with the intention of never going back. I don't know about you but for myself, I have this highly reflective part of me who is on some level active all the time and this part tells me that the real reason I'm trying to run away like this is that I want him to plead me to come back, so I could then first tell him all the nasty things and refuse but then agree to come back because he has pleaded me and it sort of wasn't my decision. However, at the same time I know that he wouldn't go out of his way to plead me back because it is my decision after all whether I want to be in treatment with him or not.
From your writing I get that the T has responded less that perfectly to some things. It is entirely possible that this T is not skilled or experienced enough to do the kind of work you need. And I agree that you need to do attachment work. At the same time, I'm not entirely sure based on your writing whether your T really isn't unsuitable or not. I think this decision, to stop seeing her and to find someone else, would be better to do with cool head. I think it would be very useful for you to try to avoid just fleeing and go and talk to her about it and see if there is any real potential continuing with her or not.
Another thing I noticed is that you want her to pick up things that you don't clearly say out. This one is very familiar to me. I have had so many fights with my T that he isn't able to understand me without me having to say stuff explicitly. At least for me, this is something that comes from very early age - a period when the infant basically hasn't separated from her mother yet. I guess I have expected from my T the same attunement as a mother has to her infant. I have raged that my T hasn't been able to do that, although I must admit that he has tried really hard and done his best. Apparently this best isn't close enough to the real perfect attunement. I don't think I've learned this lesson yet because telling things explicitly seems to vulnerable to me. I want him to pick up things himself and tell them out loud so that I wouldn't have to say them and this way I can avoid any possible misunderstanding and rejection. But I do realise that this expectation is clearly unrealistic - people really are separate from each other and have to say to each other what they want and what they think and they might get misunderstood and also rejected during that process. The therapy environment can help to learn that even if this happens it will still be ok and nothing catastrophic will happen. But as I said, this is still work in progress for me.
Also, you asked her to start working with you according to a model. I don't know what model you are talking about but I personally don't believe into working according to a model in deep psychotherapy. Sure, the therapist should have some framework to lean on but otherwise the therapy is basically just the relationship between two people and I would say that this is especially true when you are otherwise very avoidant. What happens in that relationship is determined by how the two participant perceive and feel that relationship at any moment. I don't think you can do any kind of deep attachment work following particular guidelines of a model. However, if your T is complaining that you don't want to talk about anything else other than your relationship then it might really mean that she lacks the wider framework to do the work you need and in that case it might be very dangerous if she would start blindly applying the principles of some model of attachment work to you. In that case it would be really better if you would find someone who is comfortable with transference, attachment and working with the relationship.