For another angle on this, the information being quoted in the original post might simply be wrong. (To the degree pure fiction can be wrong or right, that is.)
The Star Fleet Tech Manual doesn't specify any years of commission or years of service. It only gives stardates of authorization. The earliest such stardate is 0965, while the latest is 5099. From the rate of stardate progression in TOS, all of the dates would probably fall within Kirk's five-year mission, that is, 2266 through 2270.
Novels and various other sources disagree with that, indicating much earlier construction dates than "just before the first episode of TOS". I have never heard of 2245, though: traditional fan material gives the first Hermes, Saladin and Ptolemy vessels in the 2220s already. Same material says the Constitutions date back that much, too, which was probably the original intention when Roddenberry specified the ship as having some history before Kirk comes along. And FJ does give all the ships a similar stardate of authorization, in the 0900 range.
More modern material insists that Kirk's ship is a product of the 2240s, yet this is the first time I have heard that the other FJ ships would get moved two decades to the future as well.
If we decide to believe the wording that the class was "commissioned through years XXXX-YYYY", my vote goes for the idea that ships of the class received their commissions during those years, and kept them until retirement, which might have come long after year YYYY. The first Hermes would then have been launched some time before XXXX, put through her paces, and approved for service, at which point there would be a commissioning ceremony. And the last Hermes to be built would have been launched some time before YYYY, and would have received the same treatment.
Timo Saloniemi