Perhaps Trek adventures don't take place on a weekly schedule, split up by seasons in-universe? Maybe there was a year between "Skin of Evil" and "The Child" or whatever S02E01 was.
We know from The Neutral Zone that it was 2364 at the end of season 1. The very next episode had Guinan in.
We know that Picard said, around Stardate 45020:
PICARD: Tasha died, a year before you came on the Enterprise. You never met her.
Which means Guinan arrived between the events of Skin Of Evil (SD 41601) and The Child (SD 42073).
"A year before" seems fine for "6 months before", especially when talking about events 3 years earlier when bigger things were on their mind.
We also know that Crusher was away for about a year, and left between SD41986 and SD42073
SD 43125: CRUSHER: Well, it's nice to be together again. I was at Starfleet Medical for a year. I missed about two inches of him.
We also know that various time anchors before and after season 2 fit in with 1 year per season
But yes, I can't see any reason that stardate 41601 was in January 2364 and 41986 was in December 2364.
N.B. just saw the original FASA chronology
* The first contact with Vulcans is in 2063
* First contact with the Klingon Empire in 2151.
Those two points were kept in First Contact and Enterprise, which I never realised before. Okuda's chronology in the 90s used different dates (2161 and 2218), but canon payed homage to the first chronology, fair play.