It's not clear to me exactly what your position is, so I will assume you're a thirder. If this is not the case and I have misinterpreted your position, feel free to correct me at will.
I disagree with you because I think that "subjective probability" is indeed what one should be asking, because only in this way one can believe different things depending on the bet made.
For example, let me attack your Monty-halled SB:
If the thirder was always the correct answer, one could calculate that the red branch gets beforehand a probability of .999999, so the SB would always bet on the red and lose on average on the 'halfer' beauty.
the sleeping beauty must decide beforehand
You've changed the problem to suit your answer.
A friend referred me to another paper on the Sleeping Beauty problem. It comes down on the side of the halfers.
I didn't have the patience to finish it, because I think SB is a pointless argument about what "belief" means. If, instead of asking Sleeping Beauty about her "subjective probability", you asked her to place a bet, or take some action, everyone could agree what the best answer was. That it perplexes people is a sign that they're talking non-sense, using words without agreeing on their meanings.
But, we can make it more obvious what the argument is about by using a trick that works with the Monty Hall problem: Add more doors. By doors I mean days.
The Monty Hall Sleeping Beauty Problem is then:
The halfer position implies that she should still say 1/2 in this scenario.
Does stating it this way make it clearer what the argument is about?