Thank you for a very comprehensive reply.

In terms of clarity of meaning, I have to say that I don't feel too bad about not spelling out that the utility function is just what you would normally call your utility function

That's fine. However, normal utility functions do have self-interested components, as well as parochial components (caring about people and things that are "close" to us in various ways, above those which are more "distant"). It's also true that utilities are not totally determined by such components, and include some general pro bono terms; further that we think in some sense that utilities ought to be disinterested rather than selfish or parochial. Hence my thought that SUDT could be strengthened by barring selfish or parochial terms, or imposing some sort of veil of ignorance so that only terms like u(+NotMe) and u(-NotMe) affect decisions.

Allowing for self-interest, then in the counterfactual mugging scenario we most likely have u(+Me) >> u(+NotMe) > u(-NotMe) >> u(-Me), rather than u(+NotMe) = u(-NotMe). The decider will still be inclined to pick "H" (matching our initial intuition), but with some hesitation, particularly if Omega's coin was very heavily weighted to tails in the first place. The internal dialogue in that place will go something like this: "Hmm, it was so very unlikely that the coin fell heads - I can't believe that happened! Hmm, perhaps it didn't, and I'm in some sort of Omega-simulation. For the good of the world outside my simulation, I'd better pick T after all". That's roughly where I am with my own reaction to Counterfactual Mugging right now.

Against a background of modal realism or a many-worlds-interpretation (which in my opinion is where UDT makes most sense), caring only about the good of "our" world looks like a sort of parochialism, which is why Counterfactual Mugging is interesting. Suddenly it seems to matter whether these other worlds exist or not, rather than just being a philosophical curiosity.