I think I've come up with a simpler way to characterize Chalmers' two-dimensionalism. A core idea is modal rationalism: the contents of possible worlds are a priori knowable (on ideal rational reflection). The only thing the ideal agent doesn't know a priori is which world is hers. Her only fundamental lack is this self-locating knowledge; from that, she could know all. (It's like a multiversal version of Lewis' Two Gods.)
The ideal agent can know all world-indexed qualitative facts, i.e. facts of the form "P is true at w", given in a semantically neutral "qualitative" language. That is, expressions must have identical primary and secondary intensions. Intuitively: descriptions good, rigid designators bad! The idea is to ensure that one can know the full meaning of the terms without needing to know which world is actual. Thus "watery stuff" is okay, but "water" is not. We can know that the former picks out both H2O and XYZ, without needing to know whether we live on Earth or Twin Earth. The term 'water', by contrast, requires this empirical knowledge in order to determine which of H2O or XYZ it rigidly designates.
Okay, so our semi-omniscient being knows pretty much everything except for what world she's in (and hence what rigid designators like 'water' refer to). And she knows all this a priori. So all a posteriori sentences must in some sense depend on one's location in modal space. They depend on which world is 'actual' (in the indexical sense, i.e. which world is ours).
We can now clearly see the problem diagnosed in my post Misusing Kripke; Misdescribing Worlds, i.e. why a posteriori necessities are generally uninteresting. Our ideal agent can see all the possible worlds, she knows just what they're like, in qualitative terms. So she knows what is "necessary" in any interesting sense. She just doesn't know how to describe it using rigidly designating terms. (You might think of her as a practising Descriptivist!)
Moreover, this ideal agent would surely know any ethical truths there are to know. (She doesn't need to know which world she's in for this. Her location is quite irrelevant to the question of whether some particular action was wrong.) And this conclusively refutes Synthetic Ethical Naturalism (or any other a posteriori meta-ethic).