Although I believe that writing can often bring clarity and even transformation and that's a reason to do it, I don't think that a potential T is going to want to read something you wrote. They are not going to do therapy with you via writing, and they will still be interested in how you communicate in person.

I think there can be a lot of rejection from therapists without it being anything personal at all. I've searched for new therapists twice and even the number of phone calls made to the number returned is really quite low. And I think that even though there are plenty of bad therapists out there, I shudder to remember some of them that I have interviewed, I think that the fit between therapist and client is really important. I think I would see most of the reaction as you've been getting as not so much rejection of you as a person but the T's honest assessment that they don't think they could work effectively with you-- that either their skills or who they are as a T is not what they think you need.

Otherwise, I think that certain behaviors like challenging you to take responsibility for your life are a way of them testing to see if they can work with you. They may be looking for you to be open to change as much as anything else, also as a window into exploring your willingness to change. I think if you could see these experiences you have had as an opportunity to learn about yourself rather than as revealing some deficiency you have, that might help you.