This is a very admirable effort! There are surprisingly few cases actually made against JKR; lots and lots of charges, but very few careful cases. It's great that you've taken the effort to make one!
Unfortunately, I, at least, don't find the argumentation very convincing.
The strongest part is documenting JKR's association with people whose views seem straightforwardly transphobic in that they go out of their way to be anti-trans (in a way that, apparently JKR is not, because otherwise you might have given examples). The caveat is that guilt by association isn't very strong guilt, especially since the first association was not clearly distinguishable from "the consequences are too severe for the transgression".
The weakest part is arguing about bathrooms, where you give an example that shows that gender-specificity of bathrooms is in practice pretty strongly policed by people there, and then conclude that "Men have always gone inside women's restrooms". It rings pretty hollow. You couldn't have stayed there, waiting to prey on vulnerable men once you got the right opportunity--you were kicked out right away. JKR is very clear in the quote about specifying people who do not pass as women, so your discussion about Blair White doesn't match. JKR was talking either about trans women who don't pass, or men pretending to be trans to gain access to women. I'm not sure what JKR's position is on which bathroom should be used by passing trans women (especially ones who have had bottom surgery). Do you?
Anyway, I think the angle to take here would have to be not that bathroom-exclusivity isn't policed (it is--it's policed by users of the correct gender, as you found out), and not that men would do it anyway (because given policing, it seems reasonable that this would substantially reduce the rate), but rather that it's so rare that even if men no longer have the bathroom-exclusivity-policing to worry about, it still wouldn't be a relevant concern compared to the needs of trans people. For instance, if there's no issue with mixed-gender bathrooms, there's no issue. Heck, then everything can just be mixed-gender bathrooms! Problem solved!
The least clear part is that I think you made a reasonably-well-justified case that JKR is trans-exclusionary in that she wants some cis-woman-only safe spaces, but you didn't make much of a case that this is inappropriate at least if it's not trans-phobic so much as male-anatomy-phobic.
You can completely flip the arguments around, which I will do since JKR isn't here to argue the point, and I might be able to imagine her point. (But I can't quite express it the way she would.)
Why should a woman who has had traumatic experiences at the hands of men have to be anywhere as a "woman" where she is liable to be subjected to visceral, visual scenes that will trigger memories of these traumas in order to assuage the gender dysphoria of people who hardly need to do anything physically in order to be "not dysphoric" and are likely to be attracted to women (most trans people are not straight)? Really? That's the balance you're arguing for? Resilience is well and good and all, but if it's fair to say, "Well, just don't be triggered. Deal with it," in one of the most extreme cases of trauma that still commonly exists in our society, then nobody else really has any standing to be triggered by anything. Just tough it out. Unless the message is, "women's trauma doesn't matter because they're just women," if women who have suffered abuse can be expected put up with that, anyone can put up with whatever. Just tough it out.
So this seems like a pretty strong argument that either this isn't transphobia, or it is transphobia but it is justified because it's literally a phobia and trans people are insisting they have to be allowed to trigger it instead of finding a way to not.
The best way to counter part of this is to go back to trans women who pass. Then the premise is gone, so the imagined-JKR argument doesn't work. But from what JKR said, it's not clear to me how much she'd argue against this.
It's harder to argue the non-passing, medically unaltered case. I can't think of any great general arguments, only going case by case and thinking through the details.