I think maybe we should all start saying "transperson" -- after all, it goes with "transfolx" and so on. What's sauce for the goose is sauce for the gander, etc.
I suspect that isn't exactly what is desired, though -- since then the "validation" of "man" or "woman" is lost, and the "transperson" rendered ungendered, as it were.
I think if we all started withholding the gender validation by saying the gender neutral "transperson" instead, a large part of the attraction of replacing "women" with "people" and "person" would swiftly disappear. After all, the last thing anyone trans wants is not to be gendered at all, surely?