The problem with using hyperreals for utility is that unless you also use them for probabilities only the most infinite utilities actually affect your decision.
To use your example if U(snuggle) = ω and U(chocolate bar) = 1. Then you might as well say that U(snuggle) = 1 and U(chocolate bar) = 0 since tiny probabilities of getting a snuggle will always override any considerations related to chocolate bars.
You still need a theory, a.k.a., a prior on the kind of data you expect to be compressing. Otherwise you run into the No Free Lunch Theorem.