Guy, having slept on this, I would like to stress the value of your post(s) to critiquing the way the “caring household” analogy is commonly applied in Evolutionary Creation, however it applies to your own.
On your own position, I’m not sure we’ve yet worked through to clarifying exactly what that is, and so I’m unclear the extent to which I agree or disagree on its internal consistency, let alone its content.
But I agree with you that the analogy applies very badly to randomness, and only makes any sense of divine indeterminacy via the medium of some kind of free and responsible choice (whoever or whatever is thought to be exerting it).
Yet as used by people like Darrel Falk or other BioLogians, the underlying aim of the co-creation trope is to affirm mainstream evolutionary theory, by allowing evolution to be at least partly open-ended and so “free” of the “puppetmaster God who calls all the shots”. In other words, the analogy is usually employed so that the evolutionary process can remain scientific and “natural,” and not directed by God.
But as you rightly say, since the analogy doesn’t work with the concept of randomness, what is actually being proposed is some form of vitalistic teleology in the evolutionary process. Whilst one could make some kind of case for that via (at one extreme) Shapiro’s natural genetic engineering or (at the other) panpsychism, it is nothing to do with how “mainstream™” science understands evolution, whether that be classical adaptationism or neutral theory.
So it is actually making theistic evolution into a new variation of a long-discarded Lamarckianism or vitalism that is heterodox scientifically as well as theologically novel. It makes “Evolutionary Creation” a new theory altogether, which I’m sure is not what was intended by its proponents - or in other words, as I’ve been saying for years, it’s incoherent.
And it still does nothing to explain the current BioLogos position that mankind was always intended by God to arise: an end determined from the beginning of creation arrives via a process (whether random or vitalistic) that is insisted to be undetermined. As Aquinas said, even God cannot make “Yes” be “No.”