Why do the words 'trans' and 'woman' have to be considered as separate ideas? Aren't they part of the same thing.
All women - all people - can be defined in a bundle of different ways. My wife is a woman. She's also white, middle-class, heterosexual and British, all of which are ways of defining her, and which are categories into which she could be put. And all of those adjectives tell you something about her and the way she has been socialised, the cultural influences that have helped shape her and the way she thinks of herself. They don't tell you anything about her character, or her strengths and weaknesses. But they are part, at least of who she is.
So ... if/when (please God) I transition, I will be a woman, who is also transsexual, middle-class, white, heterosexual and British. pretty much exactly the same as my wife, in fact, except for the addition of the 't-word'. And that would be about right, because my wife and I have many of the same tastes, life experiences, cultural influences, etc ... but I'd be trans, and she wouldn't be - and that would make us different ... but not THAT different.
My point is, all of us are multi-faceted. Gender is hugely important to us - all the more so because we're trans and it's so much more of an issue than it is for most other people. But it's not the only thing that defines us, not matter what sex we happen to be at the time.