Sorry for the romajii, but no IME on this borrowed computer.
I have an idea for answer to my question, but I wanted to run it by those with more experience. Given na adjectives are really nouns (compared to i adjectives and standard verbs which are both verbs behind the scenes) and kedo just means “only” and not “is only” to “to be only” we need something to play copula role, so na is doing this.
I think I read somewhere that na is some sort of strange version of desu/da. Even so, why is it nakedo and not dakedo? Thanks!