The sticking point we have is your assertion that the word physical makes no difference. The obvious implication is that physical implies that everything must comply with the physical laws of science defining the reactive behaviour of material particles.
It makes no difference as a qualifier of determinism. As I have explained several times, determinism is the notion that every event is fully determined by the set of reasons (logical antecedents) why it happened. That's it. Nothing in that says what the system is, specifically. Nothing implies that the event or its reasons need to be physical.
The physical laws of nature may or may not represent a deterministic system (if you take quantum mechanical probabilities to be fundamental, then it doesn't - but the brain may still be deterministic for all practical purposes).
As I've also said before, to the extent a system is not deterministic, it has to be random, because if the exhaustive set of reasons for an event could have resulted in several different outcomes, then the choice between them must have been for no reason at all, which is random.
If there is a non physical regime, that regime will not be determined to behave in accordance with physical laws, but will be determined by some other means...
Yes but it is either a regime in which every event is fully determined by the set of reasons why it happened, and is therefore deterministic, or not, in which case it has some random elements.
...such as spiritually induced interaction.
Which is gibberish until you say how it works.
We have no control over physical laws of science, but our conscious awareness indicates that we have control of our thoughts, words and actions. It implies a huge difference.
There you go again trying to make 'us' external to the system you're describing. The issue is
not about what we control, it's about
how we arrive at our decisions, how we work internally.
What is so hard to understand? When you make a conscious choice, there is a process that goes on
inside your mind that
results in that choice. The question is about how that process works - by the time you get to the point of exercising control, all the important stuff has already happened.