but isn't at all what I have in mind when I imagine an agent with bounded utilities
What do you have in mind?
One easy way to do this is to map an unbounded utility function onto a finite interval. You will end up with the same order of preferences, but your choices won't always be the same. In particular you will start avoiding cases of the mugging.
Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.