I’m aware that most CBT practitioners do not practice pure CBT and instead incorporate elements of psychotherapy, as you note very well. And I’m glad they do–because at least you get some utility.
I’m not sure what you are asking me for. You want me to describe how I would treat you? I’m not a psychologist; I wouldn’t treat you. But I do know I would send you to a psychologist who practiced psychotherapy, not narishkeit.