"Eli argues against epiphenomenalism on the grounds that if epiphenomenalism is true, then the correlation between beliefs (which are qualia) with our statements and actions (which are physical processes) is just a miraculous coincidence."

Supposing he does, I must point out that it is false to say that beliefs are qualia. In fact, beliefs are part of the intentional stance. That is well worked out in Dennett's book by the same name.

The intentional level can be accounted for in physical terms (See for instance "Kinds of Minds" by Dennett to see how intentionality unfolds from genes to amoebas to Karl Popper.

One could insist on being a phenomenal realist, and say that beliefs are both an intentional interpretation of a physical system that can be accounted for without the aid of qualia, and furthermore that there was another aspect of beliefs that is the experiential aspect, the qualia-ness of them.

Even holding such a position, one needs only to explain our beliefs as long as they are physically causally effective upon the world (for instance causing us to talk about qualia, beliefs, etc..).

So if there are beliefs as intentional descriptions of organisms, AND in addition beliefs as qualia, the second kind is UTTERLY unexplainable by its very nature.

There is no need to account for them, because we have no reason to believe they exist, since if they did, they would not figure in our theories, being causally inneficient.