There's one aspect of the Zombie argument that I always felt was a tough bullet to bite, though, and I wonder if you have any thoughts: While various non-causal accounts of knowledge can handle the core-analytic kind of epistemological issues about phenomenal beliefs that arise from epiphenomenalism, I often fear that it leaves us with no decent scientific hypotheses as to the evolution of phenomenal beliefs, other than the amazing luck of humans evolving to believe they are not zombies coinciding with humans really not being zombies.
The obvious counter-argument is that it's no different than the "lucky coincidence" we assume when we reject brain-in-a-vat type sceptical scenarios despite lacking any good probabilistic reasons to do so, but there's a possibly critical difference. At least if our beliefs about the external world are true there is a natural story about how we came to have such beliefs and that story involves the external world, while if epiphenomenalism is true we still have no natural story about how we came to have beliefs about phenomenal consciousness, that [the story] involves phenomenal consciousness.
The technical version of the Zombie argument doesn't commit to epiphenomenalism in the same way the more vivid "zombie world" way of telling it does, though, so maybe it's more of a problem for epiphenomenalism than for the zombie argument.
Chalmers offers a neat answer: "The content of a conscious being's direct phenomenal beliefs is partly constituted by underlying phenomenal qualities. A zombie lacks those qualities, so it cannot have a phenomenal belief with the same content." For example, my concept of phenomenal 'redness' is grounded in the phenomenal quality of redness that I experience. My Zombie twin talks about 'redness', but in actual fact his concept is empty, ungrounded. So he doesn't mean what I do by the term.
On this account, phenomenal qualities (consciousness) can influence what we believe after all. Not causally, of course, but more directly, through constitution. The physical facts alone do not suffice to fix the intentional facts (i.e. what our thoughts are about). Phenomenal properties are part of what it is to have a phenomenal belief -- a belief that's truly "about" those very qualities. So, although a zombie would make all the same noises, their words and cognitive processes (arguably not really "thoughts") wouldn't have the meaning that ours do.
So much for particular phenomenal beliefs like 'this is red'. The original challenge was to explain our general self-attributions of consciousness. Can "phenomenal properties and the capacity to have them [still] play a crucial role in constituting its content", as Chalmers suggests? Seems plausible enough; there's nothing in the zombie's mind for his alleged concept of 'consciousness' to latch on to, for example. Surely it must be empty, again. The upshot: if we weren't conscious, we wouldn't believe it after all. Sure, we would still utter things like "of course I'm conscious!" -- but they would just be so much meaningless babble.
So, zombies are incapable of any positive conception of consciousness (and thus derivative concepts such as zombiehood). But I can think of a residual problem: what of the even more general claim that physicalism is false (i.e. a minimal physical duplicate of our world is not a full duplicate of our world)? This claim involves no phenomenal concepts, and so presumably can be thought without any need for phenomenal properties -- they aren't constitutive of this belief, at least. But that leaves us with only physical factors to explain why we disbelieve in physicalism! Odd, no?
The only way out that I can see is for the epiphenomenalist to adopt the strong position that consciousness grounds all genuine intentionality, so that zombies can't have any real concepts, beliefs, or mean anything at all. This way, even our non-phenomenal beliefs (e.g. about whether physicalism is true) are partly constituted by -- or otherwise depend upon -- phenomenal properties.
[Correction: an alternative option has been pointed out to me: the belief against physicalism inherits its epistemic warrant from the phenomenal beliefs from which it is inferred. In case of zombies, there is no such warrant to be transmitted.]
Consciousness explains why we have the beliefs we do, because without it, we wouldn't have any genuine beliefs at all.