I´m currently a determinist too, because I can not even think of real processes not fully explainable via non deterministic causes, whether we know those causes or not. However I don´t think reductionism is a good way to understand the world. You say that everything can be explained in terms of the laws of physics and chemistry; and I wonder why you add chemistry at all, given that chemical processes are all jus part of an emergent level and not fundamental. More so, why the need to consider all levels of reality within the realm of physics, when they are all just emergent levels, relationships among other things that are at the bottom, or better said outside, spacetime.
I myself prefer to consider all levels as efficient causes, and not merely effects; this so because each level contributes new ways of organising energy and information, and these new interactions don´t stay in the level but communicate or radiate to the rest. You give the example of neuroscience and psychiatry, but these sciences are precisely based on studying the mutual influence among different levels. You can say that I get frightened at the sight of an armed thug because certain patterns in my neurons determine that reactions; but we can also say that those patterns exist becouse in the upper secondary level of my imagination and memory, I know that armed criminals are dangerous.
If all levels affect all levels (in different degrees), the whole picture is a universe (or meta-universe, or omni-verse, whatever the case) with many many levels of complexity and no real separation, as causes go up and down and everything interacts with everything. Now, if we accept that spacetime itself is emergent and not fundamental (as different theories claim to explain how spacetime could have a beginning), with spacetime out of the equation you only have one single object where the past and the future, the top and the bottom, do not follow one another, but co-exist and co-evolve. In a human body, you can say that everything that happen is just atoms behaving, or you can also say that everything that happens is just the manifestation, or effect, of an idea in your parents´mind. Both approaches are partly wrong, because they only consider as real and efficient one level of reality and forget about the rest, as they forget the context of the whole universe.
Reality seems to work through causal means, in a deterministic way; but considered in its totality, is acausal because Reality needs to rest on a question without answer, that is, why does Reality exists? Nobody can answer that. It just is. And it seems to communicate with itself following deterministic laws, so far as we know.