I can relate to this a lot as well. The only thing clear in my mind is that my sex is wrong.
I think the only reason it bothers me less, after 2 years of mtf HRT, is that my T is so low I don't think about sex that much.
Others seem to be able to get into the cultural aspects of gender, and seem to take comfort in conforming to their notion of the feminine or masculine ideal. But culture seems arbitrary to me. I see no reason to stop doing this and that if I like it, or to start being these other things if I'm not like that.
Very similar experience with the solo stuff as well. If I fantasize about being the female, it's exciting, but very sad, and always has been. The male role is something I can do in a detached fashion, and it scratches that itch, as it were. I think masturbation is good for helping to avoid depression, even if you have the wrong bits, if you approach it like it's a simple exercise, like a set of bench presses or something.
I've adopted the stance of calling myself "not male," or "other". I think there's much more to being female, both socially and biologically, than can be corrected in me, even if I do strongly identify with one particular component of it. But at the same time, I simply can't relate to male behavior, either.