Thanks for your thoughtful and detailed reply, Dave!
First, one minor point: I'm not sure what metaphysical inquiries you have in mind that don't concern modality. Aren't metaphysical claims in general supposed to hold with some modal force stronger than natural necessity? And if an inquiry yields a judgment construed as having that type of modal force, doesn't it concern modality?
On the main point, my basic confusion/disagreement remains: How can we get at "the fundamental structure of reality" by armchair inquiry? Here's my alternative take: When we reflect on a priori necessities, we're reflecting on the structure of our concepts. We may thereby discover what is more fundamental than what in a certain conceptual scheme. But whether that scheme matches up well with the universe is a separate question, and not one we can answer by a priori methods.
So I'll grant you this: In our conceptual scheme, phenomenological properties are distinct from physical properties. I think your work brings this out nicely. But I know you want to argue for more than that -- you believe that conceptual distinction between phenomenologial and physical reflects a real distinction in the fabric of the universe, and not just in the fabric of our conceptual scheme. And that's what I can't see discovering through a priori arguments of the sort you develop.
I think this point is at the heart of many of the criticisms of your work -- but most critics can't develop the point entirely convincingly and self-consistently because they don't reject, in general, the existence of subtantive (i.e., not merely conceptual) metaphysical truths -- so they find themselves committed, as you point out in your replies to them, to awkward notions of strong metaphysical necessity and the like.
The arguments are in The Conscious Mind are so tight, I think, that the only plausible way to reject them is to reject the basic conception of philosophy on which they're built; and few philosophers are willing to do that. It means going back to something startlingly close to Carnap -- to, that is, a very deflationary view of metaphysics. Fragments of Consciousness and David Chalmers's list of philosophy blogs