I’m a big fan of ontic structural realism in this case.

This is the correct take. It might be true that materialism is looking less and less plausible given our best contemporary physical theories, but the idea that "thoughts aren't made out of particles, therefore ghosts did it" is absurd. There's plenty of room left for naturalistic (or even physicalist) explanations. Here's a very rough sketch of a way we might cash out the differences, going from the strongest claim to the weakest claim.

• Materialism (in the philosophy of science sense, which is related to but distinct from the Marxist sense) is the claim that the only things that exist are material bodies (and, perhaps, mereological composites of material bodies). Materialism suggests that the world is constructed out of some sort of universal "building blocks," which are themselves indivisible, spatially localized, impenetrable material bodies. The atomism of Enlightenment thinkers like Galileo, Bruno, and (sometimes) Hobbes is the prototypical materialist theory, but it's still an extremely common intuitive assumption among people who don't know too much about contemporary physics, but who are uncomfortable with supernatural entities, abstract objects, and other immaterial things. I feel quite confident in asserting that materialism has definitively been shown to be false by contemporary science (for reasons outlined below). Very extreme (but somewhat naive) eliminatively-minded people sometimes end up in this position, asserting that all that exists are atoms, quarks, or something like that.

• Physicalism is more permissive than materialism. Physicalism asserts that all that exists are the entities described by fundamental physics (and possibly mereological sums of those entities). Physicalists relax the demand that all these things be material, though, and are willing to admit things like fields, forces, energy, and other stuff that is not spatially localized, not impenetrable (i.e. doesn't exclusively take up space), or otherwise not consistent with materialism. It's very, very hard to see how we can take contemporary physics seriously without at least admitting fields and forces, since these are fundamental objects of many of our best contemporary physical theories. It isn't at all plausible that, for instance, gauge fields might really be material objects at bottom, or that bosons might really occupy space in such a way that they exclude other bosons and fermions. Not all physicalists are strict reductionists (or eliminativists), but many are. Those who aren't usually see "higher level" objects and entities as being "bookkeeping devices," constructed ways to track the operation of the things physics says exists, or convenient fictions that are nonetheless indispensable for doing the kinds of things we want to do. Most of the time, they'll assert that what's really real are the objects of fundamental physics, and that other things are (at the most) second-class citizens of our ontology. Physicalists usually endorse something like Kim's causal drainage argument, and see the real "causal oomf" as being located in the objects of fundamental physics, whatever those may be. Kim is a prototypical physicalist, but so are Alex Rosenberg, the Churchlands, David Albert, Sam Harris (I think), Peter Unger, and many, many other people. It's a very common philosophical position.

• Naturalism is the most permissive of these positions, and probably the hardest to define (in part because it can get really close to physicalism). Non-physicalist naturalists relax the claim that physics is the final arbiter over what does and doesn't exist, but otherwise hold to many of the same ideas that physicalism does. Naturalists endorse causal closure, but (at least sometimes) embrace things like downward causation, genuine metaphysical emergence, holism, and other ideas that put some composite objects on equal ontological footing with the objects of fundamental physics. A naturalist might assert, for instance, that everything that exists or occurs is consistent with the rules of fundamental physics, but that those rules don't exhaustively describe what's real. That is, they might assert that any real system's behavior can be predicted by the laws of fundamental physics, but that there are interesting features of some real systems' behavior which are missed by those laws. While most physicalists believe that the laws of the higher level special sciences are in principle derivable from the laws of fundamental physics, naturalists have room to deny that claim. A position like ontic structural realism--which denies the distinction between abstract and concrete objects, and asserts that only patterns exist--is a prototypical non-physicalist naturalist position. Dan Dennett, James Ladyman, Don Ross, Cliff Hooker, Philip Kitcher, and Sean Carroll are all non-physicalist naturalists (so am I). Ladyman & Ross' book Every Thing Must Go is a great detailed look at a non-physicalist naturalist system (and a spirited defense of that position) This position is actually rather weak, insisting only on some rather mild claims like causal closure, Ladyman's "primacy of physics principle," (which states that real things can't behave in a way that's inconsistent with physics), or similarly general principles. I find naturalism more plausible than physicalism in virtue of many of the advances that have come out of complex systems theory in the last few decades, which I think have given us good reasons to think that strong emergence, downward causation, and similar ideas that seem a little at odds with physicalism are not only real, but can be given precise scientific and mathematical characterizations.

Cartesian dualism is probably incompatible with all three of these positions, but claiming that contemporary science undermines all of these is just wrong: the complexities of our best contemporary physical theories are actually reasons to endorse naturalism, not reject it.