Be very, very cautious assigning probability 1 to the proposition that you even understand what the Law of Contradiction means. 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. If you'd just had a major concussion, with severe but temporary brain damage, would you notice? Are you sure? After such damage you might claim that "if bananas then clocks" was true with certainty 1, and feel from the inside like you we're making sense. Don't just dismiss minds you can't empathize with (meaning minds which you can't model by tweaking simple parameters of your self-model) as not having subjective experiences that look, to them, exactly like yours do to you. You already know you're running on corrupted hardware; you can't be perfectly confident that it's not malfunctioning, and if you don't know that then you can't assign probability 1 to anything (on pain of being unable to update later).

Again, though, you've defined the subspace of minds which have to be persuaded in a way which defines precisely which statements are UCAs. If you can draw useful inferences on that set of statements then go for it, but I don't think you can. 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.