I'll stick with the principle

The possibility of exact description of states on both sides [conscious subjectivity, physical brain], and of exactly specifying the mapping between them, must exist in any viable theory of consciousness. Otherwise, it reifies uncertainty in a way that has the same fundamental illogicality as the "particle without a definite position".

So the only way I can countenance the idea

sometimes there's no fact of the matter as to whether something is conscious

is if this arises because of vagueness in our description of consciousness from within. Some things not only exist but "have an inside" (for example, us); some things, one usually supposes, "just exist" (for example, a rock); and perhaps there are intermediate states between having an inside and not having an inside that we don't understand well, or don't understand at all. This would mean that our first-person concept of the difference between conscious and non-conscious was deficient, that it only approximated reality.

But I don't see any sensitivity to that issue in what you write. Your arguments are coming entirely from the third-person, physical description, the view from outside. You think there's a continuum of states between some that are definitely conscious, and some that are definitely not conscious, and so you conclude that there's no sharp boundary between conscious and non-conscious. The first-person description features solely as an idea of a "screen" that we can just "dispense with". Dude, the first-person description describes the life you actually live, and the only reality you ever directly experience!

What would happen if you were to personally pass from a conscious to a non-conscious state? To deny that there's a boundary is to say that there's no fact about what happens to you in that scenario, except that at the start you're conscious, and at the end you're not, and we can't or won't think or say anything very precise about what happens in between - unless it's expressed in terms of neurons and atoms and other safely non-subjective entities, which is missing the point. The loss of consciousness, whether in sleep or in death, is a phenomenon on the first-person side of this divide, which explores and crosses the boundary between conscious and non-conscious. It's a thing that happens to you, to the subject of your experience, and not just to certain not-you objects contemplated by that subject in the third-person, objectifying mode of its experience.

You know, there's not even any profound physical reason to support the argument from continuity. The physical world is full of qualitative transitions.

it's just blindingly obvious that our bodies and minds are built up continuously, without any magic moment when 'the lights switch on'.

Couldn't you make the same argument about literally switching on a light? :-) Obviously the idea that a light is sometimes on and sometimes off is a naive preconception that we should dispense with.