The only problem I have with that theory is that Kirk and Khan both independently use the 15 years ago figure, if I remember correctly.
Both would be within their rights to round down from 17 - but rounding down from 18 or more would call for some motivation in the character to belittle the passage of time.
However, the year of "Space Seed" might easily be moved from 2267 to 2268. After all, the episode carries a "midrange" stardate of 3141, quite possibly suggesting the third year of the five-year mission (since the earliest adventures have 1XXX range dates and the latest have 5XXX range ones). We know the fifth year of the mission was in (or extended into) 2270, so both 2267 and 2268 are possible for "Space Seed". The latter would mean the mathematic-grammatically all-important step from 18 to 17 intervening years...
FWIW, the movie stardate of 8130 would justifiably be 15 years after "Space Seed", sharp, in the TNG model where a thousand dates mark a year (and where a fifth digit, denoting decades, would be used but is here omitted).