A brief response John - responsibility and accountability can only be meaningful between two equal parties and an ability to enforce in some manner judgments regarding an unwanted outcome.
On a general note, God took on all “responsibility” for all causes and our limited view of moral accountability when His Son took on the attributes and weaknesses of human beings, and without performing an irresponsible or immoral act, was willing to suffer and unjust death at our collective hands.
If this were a two party dispute, we should be held accountable. However, since God is God, we understand it as an act of Grace. It would be correct to indicate that we have a good idea from this on what we may consider as divine action.
I haven’t checked in here in awhile and haven’t read all the comments in detail but want to comment briefly on the OP. The basic reason we can’t specify the precise interaction between God and nature is that theology isn’t physics. Suppose we want to understand the interaction between two physical systems A & B. If we know the Hamiltonians (energy functions) for both, we try to find an interaction Hamiltonian that describes how they’re related. But God is not an entity within the universe that can be described in the terms physicists use.
I think that the traditional idea of God’s cooperation with creatures provides a good way to think about divine action. It’s like the way a human works with some tool. But that’s an analogy rather than a precise description. & we don’t need to be embarrassed about that because we’re always having to use analogies when we speak of God.
No, God’s causal responsibility is not always sufficient causality. But only some “guys’ Reformed version of sovereignty” would allow that answer. A theological determinist would indeed have to agree that God’s causal responsibility is sufficient causality. It is very hard to deal with the Problem of Evil from that viewpoint, though taking Universalism seriously can make it easier. But in any case, a “Reformed version of sovereignty” (broadly construed, and perhaps including Thomists) does not require theological determinism. Probably, it does require a risk-free view of providence, and at a minimum the ever-controversial “middle knowledge” of God. But that does allow us to affirm God’s causal responsibility and still deny His moral responsibility, as I just did.
We are dealing with questions of logical consistency here. If there is a significant problem of divine action, there will be one both before and after we learn about evolutionary biology. But if not, evolutionary biology can’t create one. I’m not seeing why knowledge and acceptance of evolution presents a new problem of divine action where none existed before. Or to put it another way, why should accepting evolutionary biology require one to change one’s view about whether there is a problem of divine action?