What within utilitarianism allows for selecting between these three greatest good for the greatest number?
I don't think there's anything baked into Millian utilitarianism that automatically says what to do here, but then (1) there are other kinds of utilitarianism and (2) bolting the notion of time discounting onto Millian utilitarianism ought to solve the question. Compute the time integral of time-discounted goodness for each of the three greatest goods over all time, and pick the greatest good that gives the most positive answer. [Dusts hands.]
How much time does it take to compute over all time?
The first greatest good for the greatest number for the greatest number will start "first" (by whatever measurement is applied) but ends before the second greatest good ends and doesn't last as long (in total) as the third greatest good.
The second greatest good for the greatest number will start end "last" (by whatever measurement is applied), but does not last as long as the third greatest good (in total)and doesn't start as soon as the first greatest good.
The third greatest good for the greatest number lasts the longest (in total), but ends before the second greatest good ends and starts after the first greatest good starts.
What within utilitarianism allows for selecting between these three greatest good for the greatest number?