What is the mechanical world picture?

> Laws of nature are not externally imposed influences. They are human descriptions of what we observe to happen under certain conditions. They are called laws because we have no reason to think they are ever violated. [...] Not because of any externally imposed influence but because an intrinsic property of a sphere [...]

Sure, but what you're describing is not characteristic of the mechanical world picture. It's actually more Aristotelian. Of course, Aristotelian science is not content with mere observed correlations, but with their causes; modern science more often accepts the former, because it often suffices for technological purposes. In any case, in the Aristotelian view, things have natures. Here, the nature of a sphere entails the property you've described. Sphericity is itself an abstracted nature—you don't encounter spheres-as-such in the concrete—that we can analyze to discover properties like the one you've given (in the case of sphericity, this is the province of geometry).

> However, evidence is the only way to separate reality from make-believe

Is the claim "evidence is the only way to separate reality from make-believe" itself evident? If by "evidence" you mean strict empirical, scientific data, then this assertion is self-defeating: there is no empirical evidence that can scientifically demonstrate that "empirical evidence" is the sole criterion for truth. It is a metaphysical assertion, not a scientific finding. Your position would entail that it is itself make-believe.

I would take a more nuanced view of "evidence" here.

All human reasoning ultimately rests on first principles (such as the principle of non-contradiction or the principle of causality). These foundational truths are not known via empirical evidence in the modern sense. Rather, they are self-evident once the terms—themselves drawn from the senses—are grasped. Without these non-empirical, rational foundations, the very project of gathering and interpreting scientific evidence cannot even begin.

Furthermore, the view of "evidence" as a purely neutral arbiter of reality is naive. Evidence is inherently theory-laden. Consider that experiments never test a single isolated hypothesis, but an entire web of theoretical and background assumptions. When "evidence" conflicts with a theory, it merely tells us that something within our massive theoretical web needs adjusting. The data does not interpret itself. There is a parsimony in how we try to address such inconsistencies, but that's a practical decision.

Finally, the laws of modern physics describe highly idealized models operating in highly constrained environments. The "evidence" we gather in controlled laboratory settings relies on stripping away the complexity of the actual world. To accurately map what happens outside of these artificial models, we must actually appeal to the natures of things. (I would also add that science uses methodological and working assumptions a great deal. A big one is the uniformity of nature. Would those be "make-believe"?)

> and there is not one scintilla of evidence that anything exists apart from the universe we see all around us.

It sounds like you maintain that final causality is something external, but this is a view that the mechanistic picture encourages. In the Aristotelian view, the final cause of an acorn or an oak tree, for instance, is not external to it, but inherent to the kind of thing it is. Without telos, you could not even explain why a given efficient cause results in a certain effect. Why does striking a match consistently produce fire instead of elephants or arbitrary things or nothing at all? Because the match is causally ordered toward an effect.