Okay, I think there are some terminological issues to sort out here, resulting from our divergence from AnnaSalamon's original terminology.

The discussion I thought we were having corresponds to the CSA's calculation of "woulds". And when you calculate a would, you surgically set the output of the node, which means cutting the links to its parents.

Is this where we are? Are you saying the "would" should be calculated from surgery on the "algorithm selector" node (which points to "choice of box")? Because in that case, the links to "algorithm selector" from "algorithm space" and "innards" are cut, which d-separates them. (ETA: to clarify: d-separates "box choice" from Omega and its descendants.)

OTOH, even if you follow my suggestion and do surgery on "innards", the connection between "box choice" and "omega's prediction" is only a weak link -- algorithm space is huge.

Perhaps you also want an arrow from "algorithm selector" to "omega's prediction" (you don't need a separate node for "Omega's model of your selector" because it chains). Then, the possible difference between the box choice and omega's prediction emerges from the independent error term pointing to box choice (which accounts for cosmic rays, hardware errors, etc.) There is a separate (implicit) "error parent" for the "Omega's prediction" node, which accounts for shortcomings of Omega's model.

This preserves d-connection (between box choice and box content) after a surgery on "algorithm selector". Is that what you're aiming for?

(Causal Bayes nets are kinda fun!)