It seems to me there's a simple precedent for addressing the issue, which I've mentioned piece by piece previously.
There is an analogue to the 60s civil rights movement here - making "special accommodations" for trans students separate from the cis students starts to sound a little too close to "separate but equal," which the Supreme Court has ruled by definition to not be equal. So, even the current "best fit" solution is constitutionally problematic.
But when you think about it, in the 60s, did they address the problem of separate race bathrooms by saying "black people can use white restrooms if they identify as/can pass for white?" No, they did not. What they did was they said "separate bathrooms for races is no longer a thing."
So, as I've said before, the best long-term solution here (which will probably be met with equal acrimony by some sectors) is to simply make bathrooms unisex. No men's room, no women's room. Just bathrooms. As has been previously corroborated by halforumites, there are areas of Europe that already do this and they don't have the issue.
As a consideration to those with young children, we have a "family" bathroom in addition to the standard unisex bathroom, to placate those who fear who may be around their kids in sensitive situations.
The only real reason why we think men go in the men's room and women go in the women's room is that somebody indoctrinated us to that standard when we were in kindergarten, if not earlier. If you don't stigmatize the natural human form, if you don't create a taboo about the form opposite yours, a lot of problems seem to vanish as if by miracle.
This ties in to what I and others have said, also, in that it will be a generational change. The fact of the matter is that people don't change their minds. You won't convince a 40 year old today who doesn't think transgenderism is valid, and that men and women should segregate for bathrooms and locker rooms, to really, fundamentally change his point of view. At best, you can only get him to tolerate a situation with which he does not agree. But if we stop teaching our kids from the ground up to have taboos and stigmas about the differences in human bodies, they will grow up free of the desire to break and fetishize those taboos. And the whole thing becomes a non-issue.
I expect resistance on the right, because it does away with 200+ years of American puritan cultural tradition.
I expect resistance on the left, because it removes a vehicle by which a leftist sacred cow is used as a spearhead to attack traditionalism - IE, for some people it's not really about equal accommodation, it's about forcing a conservative to "admit" that a trans-woman is a woman in fact, and demonstrating that admission by granting them access to the women's room.