The problem is that this implies that not everything can be explained in physical terms. So, this cuts against many common formulations of physicalism, such that "a complete physics can, in principle, explain everything."
I am not sure I totally agree. In the OP I suggest that irreducibility is a natural consequence of the fact that experiences are representational. I then don't think that it is coherent for a representation to be reducible to things that cannot be identified with what is being represented, like with the photo example: a photograph of Everest contains information about everest, it does not contain information about the medium the photo is on, how the photo got there, what physical processes enable us to see the information in the photo etc.
It doesn't seem coherent to me that we should be able to gleam that information if the photo was a veridical representation of Everest. That the photo doesn't contain this information is not a fault, its exactly what the photo is supposed to do. The fact that experiences cannot be reduced to the physical then is not some kind of epistemic gap that it should be possible for us to breach; no, if experiences are representational then it is impossible to explain this in the same way that a round square is a logical impossibility. We should not expect physicalism to explain this kind of thing.
At the same time, it might be possible for the physical to demonstrate this kind of thing in principle through things like machine learning where we design an architecture for some artificial intelligence and describe the information it can process, describe the limits of what it cannot process or explain. This is speculative but I think that is a plausible avenue which is a surrogate for an explanation; for instance, if we create an advance A.I., it might start to say that it has experiences that it can't explain consistent with what we say about how our own experiences are irreducible.
Obviously, someone may just say that experiences emerged somewhere along the development of this A.I. but then the interesting part would be if we can explain why the A.I. is saying these things purely through the dynamics and mechanics of its architecture without recourse to explicit experiential constructs, which is exactly how a physicalist might want to explain away the irreducibility. If we cannot help but find our experiences irreducible as a consequence of the nature of what our brains are doing, then we may have just explained away irreducibility without needing to say that this irreducibility is because the mind and brain are distinct entities.
But then what exactly is it that makes nature "physical?"
If physical facts can only describe one set of things in the world, then it seems like "physical" is a subordinate category, and that a higher category should subsume both the physical and the mental aspects of reality...
The question then becomes: what does physicalism explain that other ontologies cannot and how does it differentiate itself from objective idealism aside from a bald posit that nature is essentially "physical?"...
The dividing line would seem to be the claim that there is something that is ontologically distinct, a substance or process that is "physical," and that this physical substance/process somehow supervenes on all that is mental in a way that is relevant enough to be worth positing. That is, physicalism has to have some sort of extra explanatory value to it after we allow that it cannot explain/describe all aspects mental phenomena. — Count Timothy von Icarus
I think from my perspective, it's not so much about some kind of physical substance as the kind of models we have about the world. As you say, the idea of a physical substance is ill-defined and vague; however, the models that have emerged in the natural sciences seem to be successful and I think that is what we should follow when trying to decide the best way to describe things that actually exist.
For me, it is very explicit that physical models are constructs which have been created by us, biological machines. I am not sure scientific models allow us to do more than predict things in some type of fashion which is directly situated and embedded in our own experiences. There isn't necessarily even a strict dividing line between predictive scientific models and other types of models in our experience; in modern neuroscience, the brain is a predictive machine which mediates all our models whether in the sciences, humanities, the way we use language, folk physics, our understanding of social situations or our own mental concepts etc.
There is therefore room for all sorts of constructs in our mind and they are just that - models! For me its trying to pick the best ones for some purpose, not necessarily turning these models into concrete substances. There is not necessarily a strict difference between models we have for things in physics, chemistry, biology, economics etc, and I don't want to say these each have their own fundamental substances either. I am agnostic, even anti-realist perhaps on that kind of thing, nonetheless there seems to be a strong intuitive picture that emerges in the natural sciences about how some constructs e.g. ones in physics seem more fundamental or to have more primacy than others. The value of physicalism then is in the value and power of physics in the natural sciences.
Someone might say this kind of physicalism is difficult to explicitly differentiate from an objective idealism but then again to say you are idealist seems to me to be adding something extra on top of the advocacy of these models in the natural sciences as opposed to just taking the explanatory value of those models at face value.
Obviously all these models are actually embedded and situated in experience as has been said. The physicalist would then say that this experience is identical to the physical just that there is no coherent way of making the reduction from the information represented in conscious experiences and the models of the physical we have constructed in conscious experience, also situated in those representations. The point of the OP is supposed to be that if irreducibility can be explained away as due to the nature of information processing in our brains then the identity between experiences and the things in physics can be defended, we just have an inherent inability to explain it in the same way that a machine learning architecture has inherent limits on what it can do or how self-reference has inherent limits.
So maybe the lesson is just to abandon "physicalism" and embrace "naturalism, monism, and realism?"
Yes, I think you could view it this way though I think the argument in the OP can also be used to defend physicalism. I think it depends on someone's inclinations; yes, physicalism is poorly defined but terms like "monism" or "naturalism" are no better I don't think. Yes, maybe it would be more true to say something like we cannot access the fundamental ontologies of nature but I also think physicalism does capture something more about my inclinations than the other labels, and captures how physics does seem to take a central role in my understanding of what exists. In some ways its actually a more honest characterization of my views and attitudes than something like neutral monism