>Consciousness appears to exist outside of the physical world, in that we can describe a physical process entirely without invoking consciousness.

Only in the same ways that e.g. emotions exist 'outside of the physical world' and we are doing some work with those (e.g. we know more about the effects of hormones on them now).

I completely disagree that this is unstudiable or 'behind the veil'. We can create beings with consciousness (babies) using a purely physical process, of course there is some way to learn more.

Personally, I assume the main problem is (as it so often happens) that 'consciousness' is too loosely defined and explaining it will be easier with more strict definitions and a deeper understanding of the brain and body.