I'm not sure that epistemic 'verifiability' is really a helpful notion here, so I wouldn't call this any kind of 'positivism'. Better, I think, to define your thesis directly in terms of metaphysical reduction. For example, it seems a bit of a stretch when you write:

any statement corresponding to a state of the material universe, reducible in theory to things like quarks and photons, testable by a being who has access to the machine running the universe and who can check the logs at will - such a statement is meaningful

It's a vivid heuristic, I guess, but it looks like the underlying idea you're really getting at here is simply the conjunctive claim that (i) there is a privileged class of fundamental "base facts" that specify the contingent state of the universe, and (ii) any meaningful statement must supervene on (or be reducible to) said base facts.

I discuss this more in my old post, 'Verification and Base Facts'.

One point worth noting is that, although most folks here happen to be physicalists, there's no principled reason why a "soft positivist" couldn't be a Chalmers-style property dualist, i.e. including phenomenal properties next to physical properties in the "base facts" to which all else reduces. After all, we can imagine our hypothetical observer "checking the logs" of the universe, and seeing -- not only that chocolate cake briefly appeared in the center of the sun (being instantly consumed in a way that nobody inside the universe had any way to detect), but also that Eliezer became a phenomenal zombie for a day (in a way that nobody inside the universe had any way to detect).

Of course, you might have other reasons to reject property dualism -- I don't want to get into the zombie debate here. My point is simply that it seems compatible with the core reductionist idea behind Yvain's so-called "soft positivism". This demonstrates just how far this view is from old-fashioned positivism and its concerns about (intra-world) verifiability.

P.S. Html doesn't work. What's the comment markup code (blockquotes, hyperlinks, etc.) for this site?