Translating back Bentham's solution (or my memory of Ayer's interpretation of it) back to your question, I think the answer would be that utility functions don't change; if you are truly a preference utilitarian, then your utility function is already given by the ultimate fixed point of the iteration process you have outlined, so there is no dynamical changing.

Not sure how this solves anything though. In a society with non-utilitarian defectors, they will still end up determining the fixed points. So the behavior of the society is determined by its least moral members (by the utilitarians' own lights). Is the response supposed to be that once you do away with the dynamical changing process there is no effective distinction any more between utilitarians and defectors? That would only seem to solve things at the price of massive non-realism. There does seem to be a pretty clear (and morally relevant) real-world distinction between agents who alter their behavior (altruistically) upon learning about the utility functions of others and agents who don't. I don't think hand-waving that distinction away in your model is all that helpful.