This is an excellently-argued case!
However, while I think it's hard to argue that a genocide is completely unthinkable, I am not entirely convinced yet that you've adequately captured the intent, the likely outcomes, the cultural context, or the moon. It's a very well-argued position, and in a few years you might be saying "told you so!", but I think it's (moderately) overstated at the moment, and the biggest factor that will drive it in that direction is, ironically, the declaration of genocidal intent.
First, I want to talk about the moon a bit. You correctly point out that the map is not the territory--if people are being killed en masse, it's really really bad, whether you call it genocide or uplifting population quality. However, in the word genocide is hidden some of the deepest and most important differences of perception between people who object to trans identity and, well, reality.
Behind the idea of genocide is the concept that some types of group identity are central to one's being: one is not at liberty to physically or psychologically divorce oneself from that aspect of one's identity.
For the purposes of the text below, I am going to define a trans-identity (with dash, to make it clear that I'm using this definition) as one that occurs with strong gender dysphoria in the (apparent physiological) birth sex. I recognize that this doesn't cover all trans people, and I recognize that there are other cases (e.g. unclear birth sex). But dealing with all the variations complicates a discussion which is already complicated enough. I'm going to set all that aside for now and address only the gender dysphoria-motivated "trans-identity" because it sets the problem into the sharpest relief.
It's very hard to get any coherent message out of the anti-trans hysteria mob, but there certainly doesn't seem to be a widespread realization that "trans-identity" has that nature.
They don't recognize that trans-identity is a core identity.
This is perhaps in clearest evidence in the usage of the term transgenderism as if it were a political or social belief like communism or anarchism. As a society, we're totally cool with using violence to stop anarchists from overthrowing the government. If they don't want a violent response, they have a very clear escape route: don't try to overthrow the government. Duh.
Are we committing genocide against anarchists? No! We don't use the term because we expect the behavior--even if the anarchists group together to achieve their aims--to be something that typical people can regulate. Not everyone can successfully regulate their behavior, but if they really really can't, then when they're a danger to society, we have various ways to remove them from society.
The obsession with pedophilia is also somewhat instructive. People generally agree that pedophilia is not okay, and in many cases we ought to take children away from pedophilic parents, and that this is not genocide against pedophiles because people are supposed to be able to restrain their sexual urges in every case where sexual action is deemed inappropriate, including in case of age of the other person.
If someone thinks trans-identity is just "belief in transgenderism", and uses the mental model of anarchism or pedophilia to decide how to react, not only aren't they going to understand the charge of genocide, it will read as further evidence of mental imbalance: "I'm talking about stopping socially harmful behavior and they're imagining gas chambers. They're crazy!"
This really isn't good. That is the path to actual genocide, where identity is mistaken for intransigently stubborn malevolence, and right indulges its eagerness to solve problems with violence. Even if the actions were completely based on misunderstanding, there would still be immense blame to be delivered to the right if this were to unfold. But being able to assign blame to others doesn't bring victims back to life. It doesn't give the victims satisfying lives.
But most people on the right, even the outspoken ones, do mostly still disavow violence, so it's not there yet. Your Trans Death section does not document a dramatic number of murders of trans people--though obviously all murders are bad and hate-driven ones are especially bad given that there is no reason to assume that the murderer will not keep hating and keep killing.
Furthermore, if you calibrate the anti-trans rhetoric by the standards of anti-Democratic rhetoric (e.g. Donald Trump repeatedly called for the incarceration of his political opponent ("lock her up")), the case for systematic demonization is rather weakened. Yes, it begins with words...but...there are a lot of words about a lot of things. Climate change (still!). Hunter Biden's laptop. Censorship on Twitter. And so on.
So although I don't doubt that there are some truly malicious actors on the right (including ones who know full well it is identity, but find it repugnant, and are willing to endorse killing to remove the repugnancy), when you say that there's a long deliberate process that's going on now, it sure doesn't look that deliberate--especially with the Fox News revelations about how Carlson especially was falling all over himself to state country-damaging lies on air that would lead to better ratings. There doesn't seem to be any mastermind here. There doesn't even seem to be any plan. Just: arouse the base, get profit, win elections. Arouse the base more get more profit, lose elections, whatever. Arouse the base more, hope the Dems self-destruct, get more profit.... It's really quite tragic, looked from a particular angle: a lot of people are caught in a cycle of counterfactual outrage-generation with no way out except a bigger outrage. That doesn't make them any less dangerous, but it does make them less deliberate. (They may be steered by the deliberate, however.)
Still, the key idea that is missing is that trans-identity is a real thing, not an ideological fiction, and the reason why this idea isn't completely solid in everyone's head is mostly because for years and years and years, trans advocates have taken a big-tent approach to identity to the point where it looks like, well, like "transgenderism".
If you say, "You don't have to have a medical diagnosis, and it doesn't have to be stable over time, and you don't have to feel dysphoria, and..." pretty soon it's going to sound like "all you need is an ideological belief that male and female is all up to your personal whimsy". Sure sounds like anarchism. But with gender.
This shows very clearly a path away from the danger of mass violence.
Focus on trans-identity.
I will now stop using the term trans-identity to mean those identities associated with strong birth-sex gender dysphoria.
There is abundant evidence that for some trans people, their gender identity, and the mismatch between their identity and physiology if they haven't transitioned, is not at all a matter of choice. Call it normal, or call it a psychological disorder, or call it a physiological disorder (body didn't develop the right way), or whatever. It doesn't matter. It's who the person is. They can't step away from it any more than someone can step away from their skin color or their most deeply felt beliefs. It is a central part of their identity. It's not an ideology. It's just who they are. And they can find commonality and support by associating with other people who are the same way. So they're absolutely members of an identity group.
And you could commit genocide against that group. They're not going away except by dying, because it's who they are.
The scaremongering on the right cannot long survive an overwhelming focus on that, and that which follows strictly from it, because firstly, I don't think much of the right would even object if that were the focus, and secondly, they've already staked out a very clear position against something else.
This doesn't say which bathrooms people should use (only that they should be able to use some bathroom and be safe), it doesn't say whether trans women are women, it doesn't say whether men can give birth (because some men are trans men), it doesn't say whether trans women should be allowed on women's sports teams, it doesn't say what criteria should be required for gender recognition certificates, it doesn't say at what age hormone therapy or surgery is appropriate (just that the medical establishment should be able to determine that), it doesn't say whether trans-friendly books should be in grade school, it doesn't even say what pronouns you should use (though if someone passes it sure makes a pretty strong recommendation, and in other cases it's highly suggestive).
It does say that children shouldn't be taken away from their parents. It does say that people receiving treatment should keep getting it. It does say that people shouldn't be discriminated against. It does say that there should be no genocide.
Things are getting serious, with pernicious laws being crafted and passed that will break up families and leave people in a precarious medical and possibly psychological situation.
If you think that things are actually on the way to genocide in the United States, and you make a very compelling case that it's at least a grave danger, it's time to throw out all the existing strategies. If it's gotten to this point, the existing strategies have clearly been an abject failure. It is, then, time to start anew.
Arguing from the most completely clear, factually solid cases, where it's most important to have medical support, seems to me like a winnable strategy. If the right is all, "Needs a medical diagnosis!" then go, "Sure! Great! Yes! The more the better! How many will you pay for!" Even the right's propaganda machine can't last all that long against a sustained collision with reality, except in very unusual situations. A majority of Republicans are vaccinated against Covid, for instance.
Maybe there are other strategies. Shouting "it's genocide!", especially without linking, every single time, to a long supporting argument like you gave here does not, in my estimation, do anything but make things worse, and quickly. It's no good if you secretly know you're correct, or if there are some states where people act like you're correct but some which don't. It's only good if the people who have the least incentive to understand, but by voting can influence policy in their state, cannot avoid coming to that conclusion themselves.