It's perfectly possible that either of the two is an impostor, really. I mean, there's a statue of the Cromwell version for future generations to compare against, but while the E-D folks (at least the engineers - Riker doesn't display signs of recognition, and Troi could have been persuaded into believing just about anything in her drunken state) recognize the Cromwell man, Kirk for his part does not recognize the Corbett man! If the looks of Cochrane were actually known for certain, Kirk shouldn't be able to be confused about whether somebody looking like Corbett could be Cochrane or not.
If we assume that Cromwell is the real deal, and derive Cochrane's birthdate from that, what are the problems and consequences? Cromwell was about 55 in the movie, giving a birthdate of 2008. We can ignore this contradicting a barely glimpsed graphic in "In a Mirror, Darkly" and concentrate on what was stated in "Metamorphosis".
- McCoy says Cochrane "died", that is, disappeared, "150 years ago".
- Cochrane says he was "87 when I came here".
- The encounter takes place on SD Unknown, without in-universe clues as to where it stands relative to other TOS adventures.
- Yet TOS can start in 2266 at the earliest.
Would 2008 work? Add 87 and you get 2095. Add 150 and you get 2245. That's twenty years short of the mark at the very least.
Where to add the twenty years? 87 is exact. 150 could be 170 easily enough, though, by the usual rules of exclamations involving a figure falling on a multiple of 50. Or even 174, for that matter. (In addition, we can add some time between the disappearance and Cochrane's actual arrival, but that would act against our interests here.)
So using Cromwell's age isn't a continuity problem at all. If anything, it turns Cochrane from a Wunderkind into a more mature genius, or conversely allows him to have early ideas on space warp at an earlier date and thus affect the technology available to mankind. (Not artificial gravity, alas - that we must have at least two decades before Cochrane's birth...)
Timo Saloniemi