This is a really interesting take, but I think the problems with the activists' take is a lot deeper than this. I agree that this is part of it, but only a small part.

1. A lot of the asks--often phrased more like demands, with a dose of "you're a horrible person if we even had to say this to you"--are for prescriptive changes to language. What is "trans women are women" if not prescriptive? This falls afoul of the realities of language in another way--English mostly isn't prescriptive, it's descriptive. Telling people how they must use words (especially that they must use them a different way than historically) rubs the wrong way especially when it comes across as moralistic lecturing, not evoking sympathy.

2. Trans activists lean very heavily on gender dysphoria for justification for policies, but then want it applied in all the cases you outlined above which don't involve gender dysphoria. This is intellectually dishonest, and people who aren't inclined to be supportive will be turned off by that. Don't think they can't tell.

3. Trans activists focus on fighting the far-right, with appropriately extreme language, when it is the center that determines legislative realities, for whom the extreme language just makes the activists seem unhinged.

4. You keep claiming that the arguments are right, but the arguments almost never get presented (you give a sort of a sketch of some, but not enough to convince anyone who isn't already convinced). The claim that the arguments are scientifically correct get presented all the time. On social media, you're much more likely to find posts explaining why you shouldn't give arguments (you did it too...) than the actual arguments. Indeed, you say you can't rely upon the power of truth and reason--but that is what is most lacking. (This is not unique to trans activism; you can find it in pro-vaccine "activism" (don't cite studies showing effectiveness and bounds on possible harm--instead, belittle an effective drug that saves many human lives (just not from Covid) as "horse dewormer" because people could only get that version), climate change activism (where I have literally had people scream at me that I'm a climate change denier because I am quoting the IPCC report at them when they drastically overestimate the size of some change), etc.; being common doesn't make it any less pernicious, though.)

Anyway, I think your tactic is an effective foil. But it kind of undercuts the "trans women are women" prescriptivism, so I'm not sure how that would mesh with the current set of goals.

If trans people are going to gain and maintain the rights they need to have good lives wherever they happen to live, a lot more focus needs to be put on fostering empathy and understanding among those who are open to it (i.e. not the far right).