I think that's just hiding the internals of the non-physical part of us from view, but it doesn't change anything. I already addressed the status of non-material components of a person in my post - if they are part of the person then they are part of their state. Whether you can 'see into' that state or not doesn't make any difference to the fact that it's still part of you and still a precondition of and an input into your decisions. They may be the outcome of nothing in 'this universe' (ridiculous concept, what does universe even mean if the definition isn't, well, universal?), but they are still the outcome of something in 'a' universe and that something has state.
Even randomness or the appearance of it doesn't make any difference. A person's state might very well include a source of randomness, in fact it almost certainly does. See my comments on this elsewhere in the thread.
Separating the two bits like this lets you have your cake and eat it too; it allows for a causal explanation between a person's (comprising both their physical and non-physical) state, and their actions, but that total state (and therefore, responsibility) can't be completely reasoned about in the reality that we exist in. They appear indistinguishable from the 'uncertain decisions' you mention in your first post, but are (in the whole picture) simultaneously causal/responsibility-inducing, and completely inaccessible to some Laplace's Demon.
It's why this kind of system usually is accompanied by a whole meta-set of of punishments and rewards as well. Since there's no way to perfectly reason and judge in our system, we have to hope that someone who has access to the higher system will provide the correct judgement, being able to see the total picture of responsibility.
It's also completely untestable, for the very reasons it 'works' as an explanation at all!
Untestable theories don’t explain anything by definition. If it influences the physical world in an ongoing way, in principle it must be testable. If it’s not testable, that can only be because it is not making a difference.
What if an "out-of-this-world" thing is a part of the state? You can't observe its internal state, so you can't emulate its functioning, even if it's completely deterministic "in a different dimension". This can be literally compared to having a complex state variable and only being capable of observing its real part, or functions of it that are entirely real. (See quantum mechanics for examples of this.)
Even randomness or the appearance of it doesn't make any difference. A person's state might very well include a source of randomness, in fact it almost certainly does. See my comments on this elsewhere in the thread.