from a personal perspective, I agree with just about everything you just said BUT that does not take precedence over any applicable law.
In todays world, yes, I can see some whacko making such a claim just for the thrills. Just how does one prove their claim is real? Perceived sincerity is nothing more than a good sell of what the person wants you to see. How does a person prove sincerity and to whom do they prove it? I do recall reading at some point of the person having to have been diagnosed with GID based on a true gender dysphoria. I do not see that that made it into the law presented so, to me, the legislature kind of wimped out on that point.
As to the unisex restroom: sure, it would be nice if s/he would use it but again, this is a personal desire and not an action able to be legally mandated from what I see. Since one would presume the person involved would tend to have a better understanding of a persons feelings not being respected, maybe s/he would be open to a suggestion that while it is not required, it would help the woman feel better about the situation. Of course the response might be; well, they just need to get used to it. I am a woman and I have the right to...
To me, that is a person with real problems, well beyond the gender issues.
If such a suggestion is made, you would have to be very cautious it is not presented as the company attempting to require or coerce them to do anything.