I read the article and it seems to miss the point rather. It doesn't seem to examine properly the desire of women to use a single sex toilet - it's only based on efficiency.
I'm fairly certain that most women would be happy to queue for longer than men in order to use a single sex toilet.
In the final proposed scenario where a small number of single sex toilets are available for the bigots and a large number of unisex toilets I suspect that in reality the single sex women's toilets would have a huge queue and the unisex would be primarily men's.
Also surprised to see that article proposing unisex stalls rather than the fully enclosed rooms with sinks required by law.