The James Blish novelization of "Miri" actually did imply that the setting was quite a few centuries further on, although I'm not sure he specified the 27th. If I remember correctly, he did postulate some future history that involved the establishment of colonies, some sort of uprising, and certain colonies becoming lost afterward. (And established that Miri's planet was simply a lost colony ... his version totally ignored the whole "duplicate Earth" business.)
With only 200 years of FTL travel and ~150 years of establishing colonies, it's hard to picture how there was enough time for them to become "lost" at all.