So which axioms should I adopt?

Isn't it a bit late for that question for any human, by the time a human can formulate the question?

So, nihilism is an anti-strategic ethical system for me to adopt

You don't really have the option of adopting it, just espousing it (including to yourself). No?

But I couldn't say I was more "right" than they, except with special reference to my definition of "right" in preference to theirs.

You really could, all else equal, because all the (other) humans have, as you said, very similar axioms rather than terrible ones.