I think this is a good letter. And I do understand your obsession with this T. Transference can be powerful.

However, I am worried you will be hurt by her. And that it will set you back to interact with her any more than you already have. I honestly think that you can get over this with a new T, and that you don't need her to be able to heal and grow. I know it has to be painful to consider the idea of giving up and letting go, but maybe that's in your best interest.