So, returning to our thought experiment, spectrum inversion is actually impossible on Russellian Monism because the intrinsic categorical facts are also physical facts.

Not in the sense of the kind of facts that physics deals with.

Russelian monism struggles with Epiphenomenality: if the measurable, structural properties are sufficient to predict what happens, the the phenomenal properties are along for the ride.

Dual-aspect neutral monism is Russelian monism done right. This holds that the physical sciences are one possible map of territory which is not itself, intrinsically, physical (or, for that matter, mental). Consciousness is another map, or aspect.

This approach has the advantage of dualism, in that there is no longer a need to explain the mental in terms of the physical, to reduce it to the physical, because the physical is no longer regarded as fundamental (nor is the mental, hence the "neutral"). Although an ontological identity between the physical and mental is accepted, the epistemic irreducibility of the mental to the physical is also accepted. Physicalism, in the sense that the physical sciences have a unique and priveleged explanatory role, is therefore rejected. To take one example, since the a conscious mental state and physical brain state are ultimately the same thing, the expected correlations hold between them. For instance, mental states cannot vary without some change in the physical state (supervenience follows directly from identity, without any special apparatus); furthermore, since mental states are ultimately identical to physical brain states, they share the causal powers of brain states (again without the need to posit special explanatory apparatus such as "psychophysical laws"), and in that way epiphenomenalism is avoided.

The more familiar kinds of dualism are substance and property dualism. Both take a physical ontology "as is" and add something extra, and both have problems with explaining how the additional substances or properties interact with physical substances and properties, and both of course have problems with ontological parsimony (Occam's Razor).

In contrast to a substance or property, an aspect is a relational kind of thing. In Dual Aspect theory, a conscious state is interpreted as being based on the kind of relationship and entity has with itself, and the kind of interaction it has with itself. The physical is reinterpreted as a kind of interaction with and relation to the external. It is not clear whether this theory adds anything fundamentally new, ontologically, since most people will accept the existence of some kind of inner/outer distinction, although the distinction may be made to do more work in Dual Aspect theory. Reinterpreting the physical is a genuine third alternative to accepting (only) the physical, denying the physical, and suplementing the physical.

Zombies would also not be able to tell they’re not zombies – which leads to the disconcerting question – how do you know you’re not a zombie?

I know that I'm not a zombie since I have consciousness, which in my case at this moment includes consciousness of knowing that I have consciousness. Anything that can be conscious of knowing that they are conscious is not a zombie by definition.

A zombie would not know that it is conscious. It would also not know that it is not conscious. It would not even know that it is uncertain about being conscious or not. Knowing is a property of a mind, and by definition of "zombie" there is no mind there to know with.

Naturally a p-zombie behaves as if it can know things to all levels of external inspection, though whether p-zombies can exist is an unsettled question.

As Eliezer points out in his article here, a zombie duplicate of yourself would profess that it is conscious, when asked whether it had any conscious experience it would say “yes!” and when given tests designed to demonstrate its conscious experience it would pass

EY also thinks we are zombies wrt. free will -- we say we have it for reasons other than having it.