The crucial point arose in my introduction to two-dimensionalism. The 2-D framework shows us that we need only one space of possible worlds, and the difference between 'conceptual' and 'metaphysical' necessity is merely a matter of how we consider the worlds in question (i.e. as actual, or as counterfactual). The point is made nicely by Frank Jackson in his From Metaphysics to Ethics, pp.77-78:
What convinced us [that 'water = H2O' is necessarily true, albeit a posteriori] were the arguments of Kripke and Putnam about how to describe certain possibilities, rather than arguments about what is possible per se. They convinced us that a world where XYZ is the watery stuff of our acquaintance did not warrant the description 'world where water is XYZ', and the stuff correctly described as water in a counterfactual world is the stuff - H2O - which is the watery stuff of our acquaintance in the actual world be it watery or not in the counterfactual world.
The key point is that the right way to describe a counterfactual world sometimes depends in part on how the actual world is, and not solely on how the counterfactual world is in itself. The point is not one about the space of possible worlds in some newly recognized sense of 'possible', but instead one about the role of the actual world in determining the correct way to describe certain counterfactual possible worlds.
So the Kripke/Putnam cases do not really shrink the space of possibilities. Nobody thinks that the 'Twin Earth' world Putnam describes is an impossible one. Rather, we still grant the possibility of the world itself, but merely re-assess how best to describe it. The necessity of 'water = H2O' says less about the space of possibilities than it does about our use of the term 'water'. All the same worlds are possible as before; it's just that now we refuse to use our term 'water' to describe any of the non-H2O stuff in any of those worlds.
It should now be obvious why appeals to the Kripkean necessary a posteriori do nothing to answer the aforementioned challenges. Consider the zombie world. We are conceiving of a genuine possible world, just as in the 'Twin Earth' case. The only question is how best to describe it. Perhaps our term 'consciousness' is, like 'water', a rigid designator. But who cares about the words? Twin Earth still contains watery stuff, even if we refuse to call it 'water', and the Zombie World still lacks phenomenal stuff (qualia), even if we stipulate that our term 'consciousness' refers to some neurophysical property (and so is guaranteed to exist in this physically identical world). Redescribing the Zombie world won't make the physicalist's problems go away. There's no denying that the world itself is possible, physically identical to our own, and yet lacking something of a mentalistic sort, however we end up describing it. And that's enough to refute physicalism (excepting Russellian monism, which allows us to deny that the zombie world is physically identical to our own).
We can clarify the point by appeal to the apparatus of 2-D semantics. Kripkean sentences which are necessary a posteriori have contingent primary intensions but necessary secondary intensions. But this cannot be the case for truths about consciousness, for our qualitative concepts are 'semantically neutral' in the sense that their primary and secondary intensions coincide.
Kripke himself noticed something along these lines. While we can imagine a world where watery stuff isn't truly water, it's incoherent to imagine a world where "painy" stuff isn't truly pain. To feel painful is to be painful. Whether something counts as 'conscious' does not depend on features of the actual world. We should come to the same judgments about consciousness regardless of whether we consider a world 'as actual' or 'as counterfactual'.
See also Dave Chalmers on 'The Two-Dimensional Argument Against Materialism'.