the problem with state-machine materialism is not that it models the world in terms of causal interactions between things-with-states; the problem is that it can't go any deeper than that, yet apparently we can.

I may have missed the part where you explained why qualia can't fit into a state machine-model of the universe. Where does the incompatibility come from? I'm aware that it looks like no human-designed mathematical objects have experienced qualia yet, which is some level of evidence for it being impossible, but not so strong that I think you're justified in saying a materialist/mathematical platonist view of reality can never account for conscious experiences.