So it would appear that star dates are random numbers in TOS, and are so convoluted and inconsistent in other series, that it might as well be random.
So in my fan fiction that I am writing, I am just going to put down stuff like 1340.4, 1341.3, and 1345.4 and just have the captains log say things like, "one week into the mission, and tensions on the ship are increasing..." and "The tensions of yesterday are decreasing after my pep talk to the crew..." and "A weak after the plot, our ship is nearly at one hundred percent efficiency" and that sort of jazz.
Or if need be I'll just put down "1344.4 (2 days later)" so the reader can get a feel for the passage of time.
I remember as a kid seeing the episode where Kirk was going to be thrown into a grave, and it gave his birth and death date, and I noticed that the dates could not be based on our calender. But was never sure if there was a pattern to this new calender.
And I agree there is a certain wisdom to fictitious dates in a futuristic sci fi, so that no one calls you out on this or that technology being improbable, or this new discovery would have been made a thousand years ago. And if your show is fond of the reset button, and may air out of sequence sometimes, having a non existent date would help with continuity issues a little. No one would call out a time travel episode because they go to a planet that was destroyed a hundred years ago. "You went back in time 50 years, but that planet was destroyed a 100 years ago".