I also like the idea of relabelling as Real Feminism or Realists (or maybe Biological Feminists ???) because the problems of labelling the movement as Gender Critical Feminism are:
A) that to most of the millions of average people we want to reach outside this debate, gender just = a polite word for sex, so they have literally no idea what "gender critical" would mean - also, it has the word "critical" in it, so it just makes us sound inherently negative and mean - saying someone is "critical" is not a positive word in real life. Unfortunately, the commonly-used alternative, Radical Feminists, is just as bad, as "radical" suggests a bunch of extremist loons.
B) By calling the movement Gender Critical we effectively centre gender in our very founding statement. You don't draw attention AWAY from gender and TOWARDS sex as the main cause of women's oppression by centring something you don't believe in in your movement's name.
Fundamentally, I think we are behind the curve in terms of public framing of the debate - TRAs have had a decade to plan this and implement it discreetly before most of us noticed, and have very successfully managed to frame the debate as T as a part of the LBGT+ and thereby paint any women (or men) who object as anti-LGBT, or "transphobic".
The most effective way to campaign IMHO is not to continue to fight on their turf (no pun intended) but to reframe the debate in terms of misogyny and safeguarding, which together with homophobia are what I see as the key issues we are fighting against.
Silencing of free speech on this ie No Debate is one of the main mechanisms the TRAs have used, together with regulatory capture; longer term, the bit I find most insidious and frightening is the attempt to play the long game by altering education ie ensuring that the next generation of voters are literally unable to understand the distinction between sex and gender or the meaning of misogyny based on biological sex, as they have been brainwashed from primary school onwards. So I think fighting back against that is crucial in winning the long term war as well as the short term battles. As Mums we are particularly well-suited to battling against that and a group centred around a parenting website would carry both a moral clout and a meaningful voice in an area where our views matter, in a way we might not have in other areas of the debate. So I think that's one area we should focus on.
Fundamentally, though, I think we need to be campaigning on misogyny and the massive attack on women's rights - and we need to be doing it with very simple, pithy and completely clear statements.
The whole campaign around eg Woman is an Adult Human Female is utterly mystifying to anyone not already familiar with the debate - if you're not aware of how far the world has fallen down the rabbit hole, then it just seems blatantly obvious and a frankly insane thing to be debating. I get that in legal terms it is of course key, and defining what is meant by a woman is of course vital in winning legal cases. But in terms of winning over the majority of the public and awakening people to the dangers for women and girls at this critical juncture, we need to be pointing out very clearly and as simply as possible how women's rights are being rolled back drastically. Because to those who don't follow the debate, they have absolutely no idea that that is what is happening. They assume that the slow but gradual progress in women's rights since the 60s is continuing.
We need to get the message out and fast - possibly in a (more effective) Led By Donkeys type campaign - simple messages, widely disseminated.