The stardate for the first episode was 1312.9 the and the last 5928.5.
If you take the two first numbers of each (13 and 59) and consider them as "months since the ship left port", so the first episode would be about one year in the mission, which makes sense, and 59 would mean the last month of the epic "five-year mission".
Then each ship/mission would have its own stardate.
Not my idea, I just read it somewhere and liked it. Probably because it acknowledeges the opening speech. I love the "it's five-year mission". Gave a sense of them being really, REALLY far away from Earth, even at FTL speeds (together with sporadic lines like "Starfleet's response will take weeks") wich make Kirk more "the guy in charge".
That was lost IMO in other versions.