I really feel it's time to stop using the term trans woman. Complying with it has, predictably enough, led to "trans women are women! Trans is the adjective and woman is the noun!"
I stopped using it a year ago and now use only males who identify as trans, females who identify as trans and people who identify as trans. Further qualified as necessary (like: males who identify as trans and who may have medically transitioned, or females who identified as trans and who have detransitioned etc).
Yes, it's not as convenient as TW and TM, but it completely avoids confusion over who you are talking about. Especially since precise and logical language construction means that a trans woman is a female who identifies as trans, whereas a transwoman is a male who identifies as trans.
In written discourse some people may notice the space in the former, but in oral communication it's inaudible. So no one knows how you are using these words.
Male and female, if necessary first qualified by their definition, are so much easier for me now.
And it does make a lot of statements much more striking. The two instances of women in TWAW are can be confusing, but replace TWAW with males who identify as trans are female and the absurdity becomes clear.
(Not to some people, I know, but the radical TRAs pushing the notion that males are female are still fringe enough that you'll frequently find the ordinary TRAs denying that extreme stance even exists.)