Excellent topic.
@j_j’s approach has much to admire, a refreshing change to the usual pat stuff. But having said that, I must admit to finding it quite difficult to read. No doubt this is a result of my more analytic background.
But @Jay’s suggestion shows a way forward.
The first observation I would make is that in modern formal logic, the law of noncontradiction does not occupy a sacred place, in the way it did in older logics. Logic is no longer seen as a monolithic whole, but as a series of tools, some, but not all, of which include LNC. Its metaphysical significance has been replaced by a semantic significance.
So we have a choice of logics, some of which include LNC. There is then the potential to talk about the world using a logic that does not presume the usual truth-functional negation or that involve more truth values than just T and F.
And what this demonstrates is that logic does not tie us to a binary metaphysics.
Now choosing a binary logic of true/false might well commit one to a binary metaphysics of being/non-being, involving identity and difference, substance and property, object and subject; but we are not obligated to begin with a binary logic.
Then the first point I’d make is that logic does not tie us to a particular metaphysics.