You seem to have a mental block about the ability of the human soul to implement a conscious choice without being shackled by the physical laws of this deterministic universe.
Let's try a different approach to the same question...
You have been able to consider that conscious minds may be the result of physical processes in the brain - I know you've rejected the idea, but you've at least been able to
imagine that conscious minds are made out of something - that they have some internal "mechanisms".
Can you not see that even if you claim that they cannot be made out of physical stuff, that they still need to be made up of something? Consciousness is complicated. Something generates the stream of our internal monologue. All the hopes, fears, motivations, impulses, and all the other things that go into making a person and the "free will" decisions they make, all come about somehow. Even if it's not made up of the activity of neurons, it has to be made up of something.
So, if we could peer into the deepest most basic workings of a soul, would we find it to be deterministic?