I think your section on the reference class problem basically solves it. I would add one more hypothetical to bolster the halfer position.

Say that as the experiment begins, in the room next door, and watching through a two way mirror, Prince Charming (PC) is also about to be put to sleep. PC knows everything about the experiment that SB knows.

However, PC is told that he will be wakened _on the last occasion_ that SB is to be interviewed. In other words, whereas whenever SB wakes up, it could be Monday(H), Monday(T), or Tuesday(T), when PC is awakened it will either be Monday(H) or Tuesday(T).

Given that, and given PC knows the coin is fair, can he gain any information at all from SB's response when she's asked what was the probability that the coin landed heads? Or will he obviously say the odds are 50/50, regardless of what SB says?

Seems to me PC should always say the probability of heads is 1/2. And since it's the same coin for SB as for PC, if there is an objective "fact of the matter," that fact should be that the probability of heads was, is, and always will be 1/2.