the same consciousness that doesn't really fit anywhere in our purely quantitative descriptions of the universe.

How does it not fit in our quantitative descriptions? We can measure its activity. It behaves differently when in a coma, or when thinking about different things, or when dead. We can grow neurons and form connections with them outside the brain to do computations. We can't make anything as complex as the brain yet obviously, but we understand how it functions. What part of it doesn't fit in a perfectly quantitative description.

I'd love for some mystical thing to exist, but literally every mystical thing people have believed for tens of thousands of years has been wrong. Why should we expect any different here? Lightning isn't caused by spirits in the mountains dancing, a god throwing lightning bolts, or anything else mystical. We can't fully describe the mechanisms at work perfectly, but that doesn't mean we don't understand it. We could assume it's something mystical into the gaps because it sounds cool, but theres no reason to think it isn't something material that can be learned.