(please don't be mean to Erica, if you're mean I'll block you)
So my approach to dialogue with TERFs over petty much 2 decades was very much founded in joint interests, my strong commitments to feminism and taking women's issues and male violence seriously.
It was also based in the fact that a bunch of my feminist friends in the late 2010s suddenly turned from being pro trans into being TERFs. I know a relatively famous lesbian human rights lawyer who's life partner was a trans woman who became a poster girl for TERF orgs during that time.
The thing is that empathy for our oppressors when it is not met by empathy or our oppressors for ourselves can not transform relationships of oppression. At some point it's just extended bootlicking and we have to move on and accept the enemy is the enemy.
If I had to guess, the reason they turned from Pro Trans to TERF was conservatism, austerity and perceiving the broader growing transfeminist representation in gender based violence sectors and similar "women's sector" jobs as a threat to their power while facing pressure from stringent budget cuts.
But as soon as you decide that TERFism is necessary and the tranners are getting too uppity, you then find friends like the anti trans feminists who make jokes about killing trans women with cancer (fair play for women's original director) and get pulled into social circles slowly radicalising you
It didn't help that most trans women in a lot of those circles were habituated into accepting abuse and coercive behaviours as norms of membership in those spaces and validating anti trans instincts of cisgender feminists.
Eg the typical "if you knew what it's like to be a woman you'd understand" that was said to trans women in cisgender feminist spaces routinely around 2000-2015 and frankly far more aggressive ways of putting similarly invalidating points.
I know at least a couple of transfems who joined relationships with lesbian feminist women where they suddenly stopped really being in community with other trans women and went stealth, with the partner later coming out as a massive TERF.
And if latent transmisogyny was widespread in cisgender dominant feminist spaces, it was part and parcel with wider coercive social dynamics reasonably accurately described in Joreen Freeman's work on "Trashing". Like all of this stuff is messy & part of a wider culture of homogenising social abuse.
Anyway I'm not telling my story here as a "poor me" thing, but I have put a very considerable amount of work into dialogue with TERFs, since 2006 to about 2023 when I stopped.
With the weight of that I don't think TERFs will change except through peer pressure from other cis people and we should invest energy in conversations with people who are at the very least interested in our welfare instead.