Sex is very simple, just look at whatever you have between your legs, or take a DNA test and look at your chromosomes.
The problem for you I guess comes from trying to distinguish gender from gender roles. My guess is that gender roles are certain patterns of behavior and what not that come imposed from society; while gender is your affirmation as to what role you would develop inside society. I would also draw a distinction between various levels of gender roles; some are harmful and on their way out ("women should stay in the kitchen") while others aren't going away any time soon.
If gender roles are imposed by society (and should therefore be questioned), then why should a transgender individual feel compelled to adopt the specific, stereotypical gender roles of the gender they identify as? I think the answer is that on some fundamental level, gender roles are the natural product of the differences between the sexes. This is why trying to completely untether sex from gender is, to me, a self-defeating proposition.
The bolded part of your post is the intellectual difficulty I was talking about in my post and the thing the left doesn't want to have to deal with. Unless you're going to be a TERF the answer that makes sense is that gender is not a social construct and is distinct from sex. As the other poster I quoted said, sex is just sex characteristics, your genitalia. That's it. Gender is in the mind. If you think it's a social construct than you pretty much have to be a TERF and say a transwoman is just a man in a dress. If you think gender is something you're born with then it's possible transpeople are born with a mind opposite what their gender is. But then that also refutes a lot of feminist rhetoric. Recent research in neurology has shown differences in men and women's brains (the areas of the brain producing most emotions being larger for women is one specific one I remember reading about). It would be interesting to see if transpeople have brains like the gender they present themselves as or something in between.