“We can all agree that transwomen with a GRC are legally women”
I would not concede that much. Once you've done that, you're basically left arguing a corner for what technicalities men should have to go through before they can 'become women'.
You'll have a much stronger argument if you do not bend to the manipulative TRA framing and just Tell Everyone Real Facts instead.
Try:
Men can never be women, because being a woman isn't a 'feeling', it's a material reality.
A woman is an adult human female, a man is an adult human male. Sex is an objective reality, 'gender' is sex-role stereotypes. We should not be creating laws around sex-role stereotypes or subjective feelings in people's heads.
The very existence of 'sex' as a legal category depends on that category having an objective meaning. Self-ID of legal sex makes sex meaningless under the law, which means all sex-based protections are rendered useless. If any man can declare himself a 'woman' with no medical transition or diagnosis needed, then any man can enter women's change rooms, transfer to a women's prison, play women's sports, etc. Lawmakers need to consider the impact on the whole of society of this change, not just the feelings of individual trans-identified people.
Suggest that an analogy would be if we allowed everyone to 'self declare' their age: all our laws which depend on age as a coherent category would be rendered useless (age of consent, pension age etc). Would people be happy with that? Does that sound like good law? Why do it then for sex? There is no benefit to women or society by rendering sex a subjective 'identity' which can only be determined by the individual. It's bad law.
It's possible to support trans-identified people's right to live free from discrimination, without supporting gender identity ideology, which is sexist and incoherent, and unworkable in law and policy.
Instead of being defensive, try going on the offensive and asking trans cheerleaders:
Define 'woman' please. If you're so sure that male people can be women, what is a woman? How can a 'girl' entity exist in the body of a male child? How are you defining 'girl'? Should a male child have his puberty arrested and his gonads shrivelled by cross-sex hormones on the basis of the unevidenced belief that he has a 'girl' entity inside him? Because that is what is currently happening to children diagnosed as 'trans'.
Link to 4th wave now article as a source:
4thwavenow.com/2017/01/26/shriveled-raisins-the-bitter-harvest-of-affirmative-care/
Note that there are NO objective diagnostic criteria for declaring a child 'trans', and that transgender activists have mounted vicious campaigns against doctors who have urged caution in medically intervening in children's developing bodies. Say that adult transgender activists campaign for ever more extreme interventions in the bodies of children while refusing such treatment for themselves. Point out that most trans-identified men keep their penises and have little to no dysphoria about their male bodies - hence the reason they are pushing for self-ID.
Ask why trans activists are campaigning to demedicalise trans identity for adults, while at the same time promoting extreme medical interventions for children, including drugs that stunt their bone and brain growth and leave them sterile. Say that anyone cheerleading for 'transitioning' children should consider whether an ideology which promotes sterilising children who don't conform to sex-role stereotypes is really a progressive one.
Don't let people guilt trip or sidetrack you by wielding fake suicide stats or murder rates. Stick to your arguments about the unworkability of self ID and the sexism and incoherence at the heart of trans ideology, and if people get emotional and aggressive (which they likely will), ask them to define terms. Say, I feel like we are using different definitions of the same words here and it means the argument isn't productive. What do you mean when you say:
Woman
Man
Sex
Gender
Gender identity
Can you define any of these in a non-circular way? For instance, it's no good saying that gender identity refers to one's internal sense of oneself as a man or a woman, if you can't actually define what a man or a woman is.
Well, this turned into a long post, but I guess it needed to be to cover all the main arguments/talking points 
Finally, if you find arguing too nerve-wracking, just link to sources discussing trans ideology in a critical way, so interested lurkers can learn more. Eg, 4th wave now or this excellent article by Helen Saxby:
notthenewsinbriefs.wordpress.com/2017/11/26/when-womens-rights-are-notadebate/
Another excellent trans-critical 101 by Charlie Rae:
thefifthcolumnnews.com/2017/08/are-there-good-reasons-to-oppose-transgenderism/
Or any Mumsnet thread which you feel discusses the issue in a constructive way 