I think I've finally identified exactly where your reasoning breaks down.
You ask who owns the diamond when you're the only person on Earth, and confidently answer, "Well, you do."
But you've just assumed the very thing you're supposed to demonstrate.
Being the only person interested in something establishes that your use of it is uncontested. It doesn't logically establish that you've acquired a morally binding ownership claim that everyone who comes afterward must respect.
Those are two fundamentally different propositions.
And invoking the Law of Non-Contradiction doesn't resolve that distinction.
The Law of Non-Contradiction tells us that two people cannot simultaneously possess exclusive ownership of the same object in the same sense. It tells us absolutely nothing about which person has a legitimate claim, or whether either does.
You've confused a logical constraint on contradictory claims with a moral rule for deciding between them.
Here's a thought experiment using your own reasoning:
Suppose I'm the only person on Earth, and I desire exclusive authority over the entire planet. Nobody else's will is being violated because nobody else exists.
By your criteria, I now own Earth.
If other humans subsequently appear, they're morally obligated to obtain my permission before occupying any portion of the planet.
Is that correct?
Because if it is, your framework allows one person's unilateral desire to establish absolute property rights over everything before anyone else gets a say.
And if it isn't, you've introduced some additional limitation on ownership that your supposed logical derivation hasn't established.
You keep explaining how your preferred ownership rules would operate while avoiding the question of why those rules are objectively morally binding.
Reductionism doesn't magically transform a definition into a moral truth. Neither Plato nor Aristotle's work on essence establishes your particular theory of property acquisition.
You can define ownership however you like, but you cannot prove that your definition is objectively morally correct simply by applying the Law of Non-Contradiction to it.
That's the distinction I've been asking you to address this entire time.