Or Kirk is still assuming the Botany Bay is a DY-500, and his estimate of two centuries is based on that.
Perhaps I should repeat the quotes in the order they are spoken in the episode:
KIRK: An old Earth vessel, similar to the DY=500 class.
SPOCK: Much older. DY-100 class, to be exact. Captain, the last such vessel was built centuries ago, back in the 1990s.
So the first thing Kirk learns about the ship is that it is an Earth DY-100 class vessel, last made in the 1990s (from 1990.000 to 1999.999) of the dating system used in "Space Seed", and last in use an unspecified period later.
SPOCK: Hull surface is pitted with meteor scars. However, scanners make out a name. SS Botany Bay.
KIRK: Then you can check the registry.
SPOCK: No such vessel listed. Records of that period are fragmentary, however. The mid=1990s was the era of your last so-called World War.
MCCOY: The Eugenics Wars.
SPOCK: Of course. Your attempt to improve the race through selective breeding.
So Spock claims that the era of the Botany Bay's construction and/or use vessel's appears to have been the mid 1990s SS, or sometime between 1993.333 SS and 1996.666 SS.
SCOTT: Definitely Earth-type mechanism, sir. Twentieth century vessel. Old type atomic power. Bulky, solid. I think they used to call them transistor units. I'd love to tear this baby apart.
So Kirk hear's Scott's opinion that the Botany Bay was constructed during the 20th Century SS, and thus sometime between 1901.00 SS and 2000.999 SS.
Then McGivers tells Kirk when suspended animation was used in space flight:
MARLA: I've seen old photographs of this. Necessary because of the time involved in space travel until about the year 2018. It took years just to travel from one planet to another.
So Kirk knows that the suspended animation units would probably have been made before about 2016 SS to 2020 SS. But Kirk already knows that the Botany Bay is a DY-100 class ship last made during the 1990s SS.
Later McGivers describes Khan as:
MARLA: A man from the twentieth century coming alive.
Ricardo Montalban was born in 1920 and 46 years old when "Space seed" was filmed. And perhaps McGivers thought that Khan could have been as much as 50 years old and that he could have been born as late as the last year of the 20th century or in 2000 SS. Thus McGivers might have thought that Khan left Earth as late as 2050 SS.
But it seems more likely that McGivers called Khan a 20th century man because she thought that Khan lived his whole life on Earth in the 20th century SS and left Earth sometime in the 1990s SS. And McGivers would have a lot more information to base that on than we viewers do.
So when Khan asked how long:
KHAN: How long?
KIRK: How long have you been sleeping? Two centuries we estimate. Landing party to Enterprise. Come in.
The evidence that had been given to Kirk onscreen indicated that Khan had left Earth in the mid 1990s.
But later:
KIRK: What was the exact date of your lift off? We know it was sometime in the early 1990s, but
So Kirk now thinks - not knows - that the Botany Bay left sometime in the early 1990s, but no evidence to support that was given on screen. Thus when Kirk earlier said "Two centuries we estimate" Kirk might have meant about two centuries after the mid 1990s or two centuries after the early 1990s.
To be safe we should assume that Kirk might think the Botany Bay left some time in the early or in the mid 1990s, and thus some time between 1900.000 SS and 1996.666 SS. The "We estimate" part many be due to being certain what period the DY-100 class ships were being made and used, but not being certain how long after that a DY-100 class space ship might have been around and available.
Kirk goes on to tell Khan:
KIRK: Yes, I understand. You have two hundred years of catching up to do.
And say to Spock:
KIRK: This Khan is not what I expected of a twentieth century man.
So with the available information Kirk believes that Khan was born the 20th century, and possibly also that Khan left Earth in the 20th century, and certainly that DY-100 class ships date to the 1990s SS.
So the two centuries or 200 years seems to be a maximum estimate on Kirk's part. Kirk seemed to believe that the Botany Bay was 200 years old and than Khan left Earth about when the Botany bay was constructed or just a few years later.
So Kirk was estimating 200 years after the early to mid 1990s SS, thus putting "Space Seed" in the period of about 2190.001 SS to 2197.665 SS - if one accepts the assumption in
Star Trek Chronology: The History of the Future that 200 years means 200.00 to 200.999 years.
But if Kirk was speaking loosely enough that 200 years might mean a time span between 1000.001 and 299.999 years, then the possible date range of "Space Seed" would be between 2090.001 SS and 2296.665 SS.
And it seems to me that one should assume as wide as possible an interpretation of all the time spans given, to increase the probability that all the time spans will overlap and there will be a time span for TOS that satisfies all of the evidence.
Or Kirk is still assuming the Botany Bay is a DY-500, and his estimate of two centuries is based on that.
...I like that! Kirk does seem a little uncertain when he says the figure, and adds the caveat "estimate" to his statement too. Where's Spock when you need him?
Unfortunately, McCoy also confirms the "sleeping for 2 centuries" statement to Khan in sickbay. Was he also thinking of the DY-500s?
...[McCoy].Could have simply been repeating what he heard Kirk say.
Very true: Khan's question was " I remember a voice. Did I hear it say I had been sleeping for two centuries?" McCoy answered the question precisely!
...
Yes what McCoy told Khan is what Kirk said, so he could have been simply repeating it, or else telling Khan the most up to date information they had about how long Khan had been sleeping. But later Kirk told Khan that Khan had 200 years of catching up to do. Kirk and Co. weren't guessing about how long ago the 1990s SS were, they were just at little uncertain how long after the period when the Botany Bay would have been constructed Khan left.
