Probably preaching to the choir here, but I don't understand the conceivability argument for p-zombies. It seems to rely on the idea that human intuitions (at least among smart, philosophically sophisticated people) are a reliable detector of what is and is not logically possible. 

But we know from other areas of study (e.g. math) that this is almost certainly false. 

Eg, I'm pretty good at math (majored in it in undergrad, performed reasonably well). But unless I'm tracking things carefully, it's not immediately obvious to me (and certainly not inconceivable) that pi is a rational number. But of course the irrationality of pi is not just an empirical fact but a logical necessity. 

Even more straightforwardly, one can easily construct Boolean SAT problems where the answer can conceivably be either True or False to a human eye. But only one of the answers is logically possible! Humans are far from logically omniscient rational actors.