Someone here made the suggestion of identifying as male and using the male changing room, as the men in there at least hadn't intentionally violated your boundaries, so were safer.
The obvious problem with this is that you still don't get to have privacy.
So the thought occurred to me: What would happen, hypothetically, if you could get all the women to declare that after seeing the transwoman, they finally came to terms with their own transness and feel male.
Then go to the men's changing room, explain the situation, tell them those transmen will now all use the men's changing room, but perhaps the men feel more like women today and would like to use the women's changing room?
What would the transwoman say? Transactivists have made it quite clear that wearing a dress is not a requirement for transwomanhood anymore. Being gender fluid is considered valid.
I'd like to see their face.