The zombie argument gets its plausibility not from anything about the argument itself but from a variety of positions pre-argument that give it an antecedent probability. The best thing to do is not to play the zombie game at all; where argument is needed, attack not the zombie argument but what makes it seem plausible that zombies are conceivable and therefore possible. Or, to put it in other words: the best strategy is simply to refuse to countenance Cartesian assumptions about the mind (the pretense that self-knowledge is easy, the pretense that we have a thorough understanding of the physical side of the equation, indeed, the pretense that the physical is all on one side of the equation and the mental all on the other, etc.) and let the argument fade on its own.
That's a bit rougher than it should be; but the basic point is right. The zombie argument is not the problem; the problem is with what you have to have in place to make the argument plausible. However, it is an interesting excercise to construct arguments that link the zombie argument to these more general problematic issues. Here is an example (one of many).
(1) If a zombie world and a qualia world are distinct, microphysically identical, and both conceivable (all three), a complete and accurate description of what the worlds share does not entail any part of what the complete and accurate description of the qualia world has that the complete and accurate description of the zombie world does not.
: This is noted by Chalmers.
: Let's call the complete and accurate description of what the worlds share the "complete physical description" and the complete accurate description of what is distinctive of the qualia world the "phenomenal description".
(2) If we know that a zombie world and a qualia world are distinct, microphysically identical, and both conceivable, we know that no part of the complete physical description entails any part of the phenomenal description.
: From (1) by epistemic closure.
(3) To know that no part of description A entails any part of description B we must know that no part of either description is overlooked.
: Suppose part of the description is overlooked. Then, for all we know, the part of A that entails B may be that part of the description that is overlooked.
(4) To know that no part of either description is overlooked we must have both to examine.
: Suppose that we do not have both to examine. Then we do not know whether there is any part of the description that is overlooked. But if we do not know whether there is any part of the description that is overlooked, we do not know that no part of the description is overlooked.
(5) Therefore to know that the complete physical description does not entail any part of the phenomenal description we must have both the complete physical description and the phenomenal description.
: From (2), (3), and (4).
(6) We do not have the complete physical description.
: There are a great many things we do not know about physical facts related to conscious experience, whatever their relation to conscious experience might be. Therefore there are parts of the complete physical description we do not have.
(7) Therefore we do not know that a zombie world and a qualia world are distinct, microphysically identical, and both conceivable (all three).
: From (1), (5), and (6).
(8) A zombie world and a qualia world are distinct and microphysically identical.
: Suppose a given world A and a given world B are not microphysically identical. Then at least one of the two worlds is not either the zombie world or the qualia world as understood in the zombie argument.
: Suppose a given world A and a given world B are not distinct. Then at least one of the two worlds is not either the zombie world or the qualia world as understood in the zombie argument.
(9) Therefore we do not know that a zombie world and a qualia world are both conceivable.
: From (7) and (8).
: Unlike the two features in (8), conceivability is not a stipulation for the purpose of describing the zombie world and qualia world but is, so to speak, the load-bearing feature of the zombie argument.
Note, incidentally, that it is not an anti-zombie argument. It doesn't take any stance whatsoever with regard to zombies. Instead it is an anti-zombie-argument argument.
