Earlier quoted context omitted.
I'm not sure you know what you've bitten off. What does your question even mean? What aspect of "post-modernism" are you hoping to tear down? One assumes you're referring to hopelessly abstruse liberal arts senior theses, and is left to wonder whether you're aware of e.g. postmodern architecture. Deliberate, original works of postmodern literary theory might be incomprehensible, but the ideas of postmodernism --- met…
What does your definition even mean? On that basis you could claim almost anything as "postmodern". It's so vague as to be utterly meaningless. I assert that we would have remixes even if postmodernism had never become a thing. Prove me wrong.
- Music went from pristine classical chords to overlapping remixes of existing music;
- architecture went from symmetrical glass boxes to crooked chaotic dissonance;
- visual arts went from seeking the perfect form to an acknowledgment that just about any form can be perfect for the right time/viewer/artist/etc.;
- morality went from religious absolutism to moral relativism;
- even physics went from clean equations that worked everywhere to requiring the observer's viewpoint to be considered (relativity) and more extreme, accepting randomness and unknow-ability as inherent principles (quantam mechanics).
Are these cultural changes related at all? You may say no, each is it's own independent thing that happened for its own separate reasons. But even if that's the case, there are definitely some commonalities among them, chiefly that "value" or even "truth" is far more complex and uncertain than we previously thought.
So to answer your question, yes remixes could exist without postmodernism. But I wonder if postmodernism could have existed without remixes.