Somehow, Chekov was conveived much, much earlier.
Much
later. Four years later, to be exact. Chekov in these movies is younger than ever.
(And of course this means that Nero's butterflies would have had four extra years to do their magic. Perhaps Pavel's parents just swapped the names of their two sons, and
again Pyotr got killed by Klingons.)
Even if the trauma of the attack is what caused Winona to go into labor early the baby wouldn't have been born for hours
How so? From the first observable contractions to birth, the process can take as little as a quarter of an hour - I've seen that happen to a second-timer. Is there some sort of a mandatory waiting period between trauma and the onset of contractions?
The ship was 1 light year outside the Klingon Neutral Zone
This doesn't work well with the actual movie, because the Klingons there are mere 75,000 kilometers from the heroes. Neutral Zones supposedly disallow the passage beyond, or even presence within, of ships, so the Klingons being that close should cause quite a bit of alarm, yet the distance in fact is quoted as reassuring.
It might be better to assume that there is no Klingon Neutral Zone in existence, so a Klingon ship tailing our heroes at such point blank range would be just another regular Cold War occurrence, no different from Russian subs tailing (and tailgating!) US boomers or vice versa.
Or then the walla in the movie meant something different altogether. Perhaps the "Could this be Klingon?" -> "Negative, you're 75,000 km from the-" exchange might mean that the heroes are close to some place that Klingons avoid like plague, and therefore Klingons can't be behind the stormy conundrum?
Timo Saloniemi