The "world state" of ASH is in fact an "information state" of p("heads")>SOME_THRESHOLD

Actually, I meant p("heads") = 0.999 or something.

(C), if I'm following you, maps roughly to the English phrase "I know for absolutely certain that the coin is almost surely heads".

No, I meant: "I know for absolutely certain that the coin is heads". We agree that this much you can never know. As for getting close to this, for example having the information state (D) where p("heads") = 0.999999: if the world is in the state "heads", (D) is (theoretically) possible; if the world is in the state "ASH", (D) is impossible.

Can you give me some examples of the kinds of cases you have in mind?

Mundane examples may not be as clear, so: suppose we send a coin-flipping machine deep into intergalactic space. After a few billion years it flies permanently beyond our light cone, and then flips the coin.

Now any information state about the coin, other than complete ignorance, is physically impossible. We can still say that the coin is in one of the two states "heads" and "tails", only unknown to us. Alternatively we can say that the coin is in a state of superposition. These two models are epistemologically equivalent.

I prefer the latter, and think many people in this community should agree, based on the spirit of other things they believe: the former model is ontologically more complicated. It's saying more about reality than can be known. It sets the state of the coin as a free-floating property of the world, with nothing to entangle with.