How confident are you that logic works like you think it works; that you're not just spouting gibberish even though it seems from the inside to make sense.

I'm not even 90% sure of that, but I am entirely certain that the LNC is true: suppose I were to come across evidence to the effect that the LNC is false. But in the case where the LNC is false, the evidence against it is also evidence for it. In fact, if the LNC is false, the LNC is provable, since anything is provable from a contradiction. So if its true, it's true, and if it's false, it's true. So it's true. This isn't entirely uncontroversial, there is Graham Priest after all.

Particularly worth noting is that there's no way any "should" statement can be a UCA because I can have any preferences I want and still fit the definition, but "should" statements always engage with preferences.

I'll channel Kant here, cause he's the best UCMAist I know. He would say that almost all 'should' statements involve preferences, but not all. Most 'should' statements are hypothetical: If you want X, do Y. But one, he says, isn't, it's categorical: Do Y. But there's nothing about 'should' statements which a priori requires the input of preferences. It just happens that most of them (all but one, in fact) do.

Now, Kant actually doesn't think the UCMA is UC for every mind in mind-space, though he does think it's UC for every mind capable of action. This is just to say that moral arguments are themselves only applicable to a subset of minds in mind-space, namely (what he calls) finite minds. But that's a pretty acceptable qualification, since it still means the UCMA is UC for everything to which morality is relevant.