Hi CE,
I'm glad you've come up with a list of qualities you feel are important in a t! I'm doing a similar thing myself.
And to me, it makes sense that you'd list codeling if by that you mean very warm and nurturing in a way, as in you can feel their caring very much. You mentioned before not being able to feel that current t supports you. I agree about hankster's idea of a child or adolescent t. And I don't think the nurturing approach and skills based are necessarily in conflict if the t is very flexible.