The French experimental philosopher Florian Cova has now written an almost absurdly thorough and thoughtful response to the earlier discussion of experimental philosophy by Pascal Engel.
One of the main themes of Cova's response is that when you take the time to look at the actual published papers in experimental philosophy, what you find is that most of these papers are not at all committed to the metaphilosophical views that Engel criticizes. In fact, many of them seem not to be taking any stand at all on metaphilosophical questions (concerning philosophical method, the psychology of intuition, etc.); they are entirely devoted to the kinds of first-order philosophical questions that draw people into philosophy in the first place (questions about free will, the nature of consciousness, the existence of objective moral truths).
Cova illustrates this point with a nice example (once again, in my amateurish translation):
A good example of this use of experimental philosophy is a recent article by Strandberg and Bjorklund on moral internalism. In this article, the authors (one of whom is a moral philosopher of the most classic sort) examine certain arguments used by defenders of moral internalism that rest principally on an appeal to intuitions. They reject these arguments, claiming that the intuitions taken as premises turn out not to be widely shared. Their aim here (as in many of Strandberg's non-experimental articles) is simply to determine which is the better position -- moral internalism or moral externalism. There is no larger psychological aim, nor any pretension of giving methodological lessons to the entire philosophical community. It is simply a matter of using an argumentative tool in order to defend a view within a specific debate. An objective that is very philosophical, all in all.
Regardless of what you think of Cova's specific conclusion, I think his basic methodology is right on target. Surely, if you want to reach a better understanding of experimental philosophy, the best method is an empirical one! PhilPapers now lists 565 papers in experimental philosophy. So if you want to know what sorts of philosophical commitments experimental philosophy papers typically have, the best approach is just to pick a few at random and try reading them. (Of course, it might be quite difficult to determine what sorts of implicit metaphilosophical commitments these papers have -- the point is just that the only way to reach a proper understanding of the experimental philosophy movement as a whole is to grapple with the details of the various papers that make it up.)