I still have the perception that this T is just way too cognitive for the work you want and need to do.

With another T it could be completely different. Probably you would benefit from a T who has very firm but yet not static or inflexible boundaries. The T might refuse to tell you that he cares about you but he would let you rage about it and in this interaction he would be able to convey you that although he doesn't say the words, nevertheless he truly cares about you deeply. And that would help you to calm down and take that in. And then you would have something that you did not have before.

Right now it stays on the cognitive level - you discuss and argue but you don't seem to get from these discussions what you need.

This is just an example because I would not put that much emphasis on a particular set of words but there are infinitely many things that need to be processed both on cognitive and much deeper level, whereas the full cognitive processing might start to make sense only after something important and meaningful has clicked on a deeper level.