First, thanks for having this conversation with me. Before, I was very overconfident in my ability to explain this in a post.

In order for the local interpretation of Sleeping Beauty to work, it's true that the utility function has to assign utilities to impossible counterfactuals. I don't think this is a problem, but it does raise an interesting point.

Because only one action is actually taken, any consistent consequentialist decision theory that considers more than one action is a decision theory that has to assign utilities to impossible counterfactuals. But the counterfactuals you mention up are different: they have to be assigned a utility, but they never actually get considered by our decision theory because they're causally inaccessible - their utilities don't affect anything, in some logical-counterfactual or algorithmic-causal counterfactual sense.

In the utility functions I used as examples above (winning bets to maximize money, trying to watch a sports game on a specific day), the utility for these impossible counterfactuals is naturally specified because the utility function was specified as a sum of the utilities of local properties of the universe. This is what both allows local "consequences" in Savage's theorem, and specifies those causally-inaccessible utilities.

This raises the question of whether, if you were given only the total utilities of the causally accessible histories of the universe, it would be "okay" to choose the inaccessible utilities arbitrarily such that the utility could be expressed in terms of local properties. I think this idea might neglect the importance of causal information in deciding what to call an "event."

Different counterfactual games lead to different probability assignments.

Do you have some examples in mind? I've seen this claim before, but it's either relied on the assumption that probabilities can be recovered straightforwardly from the optimal action (not valid when the straightforward decision theory fails, e.g. absent-minded driver, Psy-kosh's non-anthropic problem), or that certain population-ethics preferences can be ignored without changing anything (highly dubious).