That would do it, though it may only attack a straw man: the thesis that the, say, categorical imperative is universally compelling is not the thesis that the CI is universally persuasive. Rather, I think the thought is that we are all rationally committed to the CI, whether we know or admit this or not.
Taboo compelling and restate. If compelling does not mean persuasive then what does it mean to you? Also taboo "committed" and "rational" - I think there's a namespace conflict over your use of rational and the common Less Wrong usage, so restate using different terms. As a hint, try and imagine what a universally compelling argument would look like. What properties does it have? How do different minds react to understanding it, assuming they are capable of doing so? For bonus points explain what it means to be rationally committed to something (without using those words or synonyms).
Also worth noting: P1 is a generalization over statements about minds, not minds.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.