The only mention of the Enterprises age is in TSFS ("The Enterprise is 20 years old") and it is hard to reconcile with other data points.
Here, I'll admit to having to fudge, but I always though Morrow was talking about the age of the Enterprise
since her refit (which would be fifteen or sixteen years) and rounded up for emphasis.
Except it must a lot less time than that since the refit seen in TMP.
TSFS happens maybe weeks after TWOK, which happens approx 15 years after Space Seed. Space Seed was in the first year of the 5YM (assuming a season = a year and season one is year one). The refit was launched to intercept V'Ger 2.5 years after the end of the 5YM.
Year 1 - 5ym starts, SPace Seed
Year 8 (or 7.5 to be exact)- Enterprise refit launched to intercept V'Ger
Year 15 - TWOK/SFS
So, by this reasoning, the refit was only seven years prior.
You just have to fudge in a way that's satisfactory to your view of the universe.
Working backwards from the 2364 date given in The Neutral Zone
, the trilogy would take place in roughly 2286. The refit was complete somewhere around 2271.
Khan had been trapped on Ceti Alpha V without access to any kind of time-keeping devices (from the looks of it) and in a perpetual sand storm. I figure he just didn't have an accurate way to gauge exactly how long he'd been there after Ceti Alpha VI exploded.