But if there is a way in which consciousness works, we certainly don't know how it works. Why then should we expect to be able to discern the identities in a scheme that we're basically clueless about?

As we mentioned elsewhere, Berkeley had no idea--could not possibly have had any idea--about ion channels, about conformational change of molecules upon being excited by absorbing a photon, etc. etc.; and yet this is what you need to have a satisfying account of how the external world gets translated into our heads. That we weren't imaginative enough to envision it prior to centuries of painstaking experimentation is a statement about our powers of imagination, not the ontology of the world.

Furthermore, we now understand that computational systems are all equivalent, and that the brain's operation is at least largely a computational affair, so all finite computational solutions are also in bounds.

What you're really claiming here, therefore, is that your powers of imagination are fully adequate to cover all possible reductive physical or computational accounts of consciousness. I could understand being agnostic, even despite the numerous pieces of evidence that consciousness is at least highly dependent upon and affected by physical interventions upon one's brain.

(Note: you claim a "brute assertion", but one wouldn't demonstrate the computational equivalence of a particular structure and consciousness by assertion, but rather by testing it and demonstrating that it has all observable properties that can be discerned from the outside, and an internal structure that plausibly supports a sense-of-things. We're certainly not there now, but if the promissory note of an explanation ever comes to pass, the brute assertion would be to the contrary: despite every indication that this is how it works, I refuse to accept that this thing is conscious, and you cannot make me because you cannot demonstrate its sensation to me in the same way that I feel my own sensation and I will accept nothing less, even if I will accept a great deal less when it comes to deciding if you are conscious.)

Now, if that is indeed your intuition: "yes, although it appears that I am making the Berkeley mistake, I am perceptive in this matter in ways in which he was limited," then I don't have very much to argue against.

My intuition is that it's best to retain some degree of uncertainty, but after a long and inglorious history of people confusing lack of imagination with lack of possibility, the wise attitude ("intuition") seems to me to be to go with the track record and tentatively accept: yeah, this too is very likely to work.