I really like this idea that you fleshed out in this post, it seems to relate more to the more common concepts of "consciousness" that are usually referenced. I do think that your description and Koch's don't necessarily have to be disjoint, it is possible that the "simple connection count" is highly correlated with this pattern of self that you have identified. The specific subsystems that you listed may just be very effective (and thus common) ways that this theme of consciousness usually emerge, though not necessarily the only ways. Disclaimer: I tend to think of this subject as more speculation than science anyways, at least currently, thus the opinions I have voiced are just that.