Many philosophers of the mind—such as David Chalmers, Galen Strawson and Philip Goff—have become sympathetic to variants of panpsychism when it comes to explaining consciousness. Yet, on their own admission, most of these philosophers note that they are trying to fit consciousness into a broadly physicalist picture. Chalmers describes Russellian monism, for instance, as a kind of "broad physicalism". Similarly, Strawson calls himself a "real physicalist" on these matters. In other words, it seems these philosophers are committed to a broadly materialist view of the universe, they've just added consciousness as a kind of feature. And they are all, it seems, adamant about a kind of property dualism: that is, that consciousness is not identical to physical stuff.
Most of the time, when I read their papers or hear their talks, they praise views like panpsychism because it "avoids" the problems of complete dualism and hard materialism. In his 2002 paper, Chalmers explicitly says that Russellian monism is a way to circumvent issues with the causal closure of the physical world. But, as far as I can tell, panpsychism in its various forms does not do this, and it still faces the age old interactionist problem.
Now, assuming these philosophers are broad materialists, they (I believe, though I could be wrong) subscribe to the view that intentionality, thought and rationality are products of the physical brain. But the question becomes, how is it that we have knowledge of our own mental states? The brain as a material body would have to inquire into its own immaterial qualitative life to even form such thoughts in the first place—which is precisely the common interactionist criticism of dualism. Now, the Russellian monist might object and say that the brain is not a classical material body, it is made up quiddities which are not purely physical in the traditional sense. But one point of being a broad materialist is to affirm that things like thought are a product of an objective kind of structure and function. To me, the available options then seem either to deny the immaterial reality of consciousness (like Dennett, who thinks consciousness is not the special phenomenon we think it is), or to commit to a full on Cartesian dualist or religious soul view and affirm that intentionality, thought and so on are not material acts at all. But if you are going to say this, you might as well throw panpsychism out because panpsychism only gives the universe bits of consciousness and experience, it does not offer fully functioning immaterial minds.
Most of the time you hear these philosophers obsessing over the "hard problem of consciousness", which only deals with how consciousness (which is not material) arises. And if you do acknowledge the "hard problem" to begin with, then you are very likely a property dualist (you deny that conscious experience—or qualia—is a simple reducible material act). And if you acknowledge this while simultaneously affirming that the functional aspects of the mind are material (e.g. thought), you're still stuck explaining the interaction issue that I discussed above.
Anyway, a bit of a long winded preface to a short question. What have these philosophers said about thought and intentionality? And have they written or spoken on these interactionist issues that I have raised as issues for panpsychism and its other versions like Russellian monism? Please correct me as I am sure to have mischaracterized their views at various points.