"The thing is that I question the ability of A to formulate a proper B". I'd call that wisdom. I tend to think of A's initial B as a first approximation. Once they get feedback as a result of their first 'move' they can revise B if needs be (always bearing in mind that continually revising B can itself be an example of 'the solution being the problem'). I agree that the "ABC set-up is implied in any form of problem solving", and this can be arranged in several ways, e.g.:
B as the problem and C as the solution.
B as the proposed solution (Penny and I call this a Remedy in the
PRO model) and C as the means to achieving B.
B as a resource and C as ways to access the resource more often or more easily or more intensely etc.
B as a resource and C as contexts in which B happens naturally.
There is also another, and to my mind very different, frame:
B is a desired outcome and C is the space of possible moves A can make, given that they would like B to happen.
I do not regard this as problem solving but creating something new (a la Robert Fritz).
By his own definition (and actions) David Grove was a "problem solver" – and a great one at that. We had several discussions about desired outcomes and I don't think I ever convinced him of their value. Actually, I don't think I ever convinced him of anything. It took me several years to figure out that wasn't my role.
Back to your suggestion. I really like the "sort of evolutionary chain of change" notion, and the (1) "formulate a first action towards B" and see what happens. Equally interesting might be (2) "formulate a first action away from B" and see what happens, and (3) "formulate a first action randomly" and see what happens.
I've attended several practice groups where we put (3) or versions of it, to the test. We tried it with the client:- throwing dice to decide where to move to
- blind folded
- using diving rods
- going where the facilitator decided.
As you might guess, all produced fascinating results.
Your "Given you at A in the context of C, is there anything you'd like to do to change C?" is a lovely idea of attending to C (and thereby taking the focus off B, although it is still involved by adjacency). I really appreciate you giving a specific example and the wording of the question doesn't quite work it for me. And the "Can, Will, Are' sequence feels a bit pushy. But I'm not sure what to suggest instead.
The 'classic' Clean Space question:
"And what do you know about C from here (A)?" could be a nice starting point.
It could be added to with:
"Given B there, what do you know about C?"
"Given B there and A here, what do you know about?"
or"And find a space that know what C would like to have happen."
I know this doesn't really address what you are aiming for but it's all I have for now. I'll give it some more thought.