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?
I think you may have some typos such as 'for the greatest number for the greatest number' in paragraph 1 and 'will start end' in paragraph 2. But that aside, if I throw in some concrete numbers:
GG1: 1 year of fun, starting today.
GG2: 1 year of fun, starting 3 years from now and ending 4 years from now.
GG3: 2 years of fun, starting 1 year from now and ending 3 years from now.
If you were to heavily time discount, you would probably pick GG1.
If you were to simply want most person years of fun, you would probably pick GG3.
If you were under the impression that this was heavily focused on a survival analysis (Dr. Dystopia, unless stopped, will cause absolutely no effects until the fun starts, and then at the end of the fun period will exterminate everyone forever.) then you might want to pick GG2, since that gives the most time to come up with a plan to stop Dr. Dystopia.
If three people all have comparable utility beliefs except that one is heavily time discounting, one is heavily valuing person years and one is heavily thinking of survival analysis and they need to vote on those scenarios, presumably they have different priors and can begin discussing the various types of evidence they have for those beliefs and can attempt to come to an accurate conclusion.
Does that help? I'm a bit concerned I'm not addressing the core question, but I'm not sure what else to say yet.