Indeed I did misinterpret it that way. To answer the other interpretation of that question,

how do you specify an (idealized version of yourself that reasons about morality without using words like "moral", "right" and "should")?

The answer is, I don't think there's any problem with your idealized self using those words. Sure, it's self-referential, but self-referential in a way that makes stating that X is moral equivalent to returning, and asking whether Y is moral equivalent to recursing on Y. This is no different from an ordinary person thinking about a decision they're going to make; the statements "I decide X" and "I decide not-X" are both tautologically true, but this is not a contradiction because these are performatives, not declaratives.