I don't want to get into detailed exegesis. But here's something for you to think about.
Clearly it's anachronistic to claim Nietzsche as a postmodernist: too early. But lots of people have claimed him as a prefigure -- postmodern avant la lettre. You think this, it seems. Have another think.
Yes God died, and so (Nietzsche thought) ethics and morality lost their ground. But it's a step further along from ethical/moral relativism to the truth-relativism of postmodernism ("chaos" as you say). I'm not convinced this was a step Nietzsche took.
Possibly he was too smart. (He was quite clever, most his life.) Of course truth can't be relative; maybe he'd have liked to think it was, but anyway it didn't work out (because it couldn't).
(Why can't truth be relative? (This is fun if you've not seen it before.) ... Here's why. "Nothing is (really, actually, definitively, absolutely ... whatever) true" is a proposition that says of itself (among other propositions, but still) that it isn't (really etc.) true. So if it's true, it's false. So it's false. (Why does that remind us of B. Russell?) And, yes, "truth is relative" is equivalent to "nothing is (blah, qualifications) true". So "truth is relative" is false. So truth isn't relative.
You might think of this as the Epimenides argument against postmodern relativism (obvious reasons). You might try to manufacture an Epimenides argument against (Nietzschean or other) moral relativism ... but it's kind of hard (essentially, I guess because of the partial reliance on disquotation or similar: works fine for 'meaning' ("nothing means anything" says of itself it's meaningless) and other semantic predicates, but maybe not (I'm not definite here) for morals/ethics and related). Don't give up, though; we didn't go to the moon because it was easy, after all.)
I'm not claiming Nietzsche thought all (or any) of that explicitly, btw (though those who enjoy exegesis might like to trawl). But anyway, not everyone agrees he was a postmodernist, even avant la lettre. (And, incidentally, much less even was he a poststructuralist, which that stuff about transcendental signified suggests you think.)