From reading your article, it seems that the flaw of epiphenomenalism goes beyond what you have stated, Eliezer. The epiphenomenalist position is that, say, a zombie sensation ZS can cause a zombie belief, ZB, while ZS causes MS, the mental sensation, and ZB causes MB, the mental belief. There is supposed to be no relation between MS and MB. Surely then, this means that all beliefs, language and logic in the mental universe, or whatever it is, are both unjustified and unjustifiable. The connection normally assumed in justifying things is necessarily absent. Beliefs must not be caused by argument, or experience, experiment, or anything else. If mental beliefs even resemble true beliefs which exist in a world where beliefs are actually related to some sort of justification, it cannot be known.
The epiphenomenalist position thus seems to resemble the skeptical hypothesis of the evil demon espoused by Descartes. All truth only seems to be true by virtue of the composition of experience. Particular phenomena are merely arranged as such to provide only the illusion of a coherent world, where in fact the illusion may be all there is. Just as Descartes' demon would decieve us such that we think we know 2+2=5, we, the epiphenomenal consciousnesses, could be decieved by the nature of our feeling into believing it. There can be no way to know whether 2+2 is or is not 5. There are only sensations arranged such that it seems that way.
Thus, an epiphenomenalist must admit that all meaning and truth apparent to us is probably meaningless and false -it cannot be known to be otherwise. So, by simply attempting to use language or logic to establish epiphenomenalism, there is contradiction. Epiphenomenalism must either be true, and so all we 'know' is probably nonsensical, or epiphenomenalism is false and the three paragraphs I just typed are a meaningful refutation.