I don't think your arguments are a posteriori or empirical because you're talking about existence in the abstract and you're trying to analyze that concept by applying some basic logical distinctions that are supposed to be exhaustive.

But what's the main point you're wanting to make, expressed in plain language? That all that exists stems from a natural force? Scientists have pretty much established that a changing natural universe exists. What is it, then, that you mean to be adding to scientific theories or to philosophical naturalism?