I recall reading part of a translation of Aristotle's Metaphysics, in which he seemed to introduce the concepts like the law of the excluded middle. It struck me he was making a point about language, rather than about reality or "the world."

Aristotle in this passage (which I could dig up) complained about Heraclitus' followers believing all is flux and "you never step in the same river twice."

If reality is in Flux (Heraclitus) or One (Parmenides) that would seem to pull the carpet out from underneath the Classical Principles you itemize (implying either nothing is A or everything is A respectively).

I think it makes sense to agree with Heraclitus and/or Parmenides, then grant Aristotle's Logic as a necessary ground for talking meaningfully about reality (versus foregoing talking meaningfully about it).