Dear George,
thank you for your interesting post, which gives to me more opportunity of talking about the principles of Quantum Theory (my joint work with Chiribella and Perinotti). Indeed, what we learn at school is that unitariety of Quantum theory is a rule, but this indeed is not true: the theory can survive without the requirement of unitariety keeping perfect thorough logical coherence, and using quantum channels (completely positive trace-preserving maps) instead. Also the motivation for unitariety that "transformations must be reversible for a closed system" is false, since, strictly speaking, for this purpose one needs the evolution to be just isometric. Requiring that the reverse of the reversible transformation is also reversible is a matter of simplicity. I think that unitariety is just for historical reasons, due to the Schroedinger equation, which, however, is needed for the "mechanics" of the theory, quantization rules and so on. If one wants a theory that is autonomous from the classical one (but from which classical mechanics emerges from pure quantum theory of systems, as for the quantum cellular automaton), then unitariety is not strictly needed for the logical coherence and closure of the theory. In the automaton, however, unitariety is dictated by the requirement of having the Dirac field emerging at the Fermi scale.
Therefore, is up to you to believe that the purification actually exists. We know that Quantum Theory allows for purification of any transformation using an environment (and by the way the purification of the postulate is an isometry, which then we know can be further extended with a unitary). But you are not obliged to have the actual purification: everything works as if the purification exists. If now you ask me for "a mechanism" for such a purification (in case you believe that there is an actual environment), that's an interesting question. Maybe one should try to describe the "informaton" as an incompressible fluid, or something similar. By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment! Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this). The true point is to decide what is spontaneous, and what is not-the chicken and the egg again.
Finally, let me say that I liked your essay very much (it was one of the first I read). I can agree with your idea of your top-down causation, within my definition of causality (axiom 1 of QT), and as a Bayesian, in the sense that since causal relations are established by parametric dependences of probabilities, in a Bayesian interpretation they are themselves "beliefs", and such they are established by us, as any theory is formulated (this also agrees with the Humean point of view of causation). And, as such, you are right when you say, "Understanding the emergence of genuine complexity out of the underlying physics depends on recognising this kind of causation".