Having looked at your diagram now, that's not quite what I have in mind. For instance, "what I attempt to implement" is kinda an "innards" issue rather than deserving a separate box in this context.

Grr! That was my first suggestion!

Actually, I realized that what I want to do is kind of weird, sort of amounting to doing surgery on a node while being uncertain as to what node you're doing the surgery on. (Or, alternately, being uncertain about certain details of the causal structure). I'm going to have to come up with some other notation to represent this. ... I'll probably have to use a crude hack of simply showing lots of surgery points and basically saying "do surgery at each of these one at a time, weighing the outcome by the probability that that's the one you're actually effectively operating on"

Not that weird, actually. I think you can do that by building a probabilistic twin network. See the good Pearl summary, slide 26. Instead of using it for a counterfactual, surgically set a different node in each subnetwork, and also the probabilities coming from the common parent (U in slide 26) to represent the probability of each subnetwork being the right one. Then use all terminal nodes across both subnetworks as the outcome set for calculating probability.

Though I guess that amounts to what you were planning anyway. Another way might be to use multiple dependent exogenous variables that capture the effect of cutting one edge when you thought you were cutting another.

Before we continue... do you have any objection to me making a top level posting for this

No problem, just make sure to link this discussion.