Let's try this, The Enemy Within was the 5th episode produced, Tomorrow is Yesterday was the 21st episode produced. In The Enemy Within two separated Kirks were beamed into a single common body.
Is it possible that that procedure is basically what we saw with Christopher and the sergeant?
In the case of Christopher, he was in his aircraft and after a brief glimpse of the Enterprise, there was nothing. Christopher suddenly "remembers" the events of the next day (or so), but he also remembers never being out of his aircraft. The integrated memories of the two Christophers are just as real.
From the perspective of the Air Force, Christopher was in contact with the ground every few seconds.
KIRK: If the Captain feels duty bound to report what he saw, there won't be any evidence to support him.
CHRISTOPHER: That makes me out to be either a liar or a fool.
KIRK: Perhaps.
This dialog from Kirk states that Kirk fully expect Christopher to remember his time on the Enterprise.
With the sergeant, he patrolled a corridor to a point outside the statistical services office, suddenly he "remember" the next several hours. Seeing a light in the office, confronting two men, being in a strange room, being served soup. But he also distinctly remembers that he just walked up the corridor a few seconds before.
No missing time, no erased memories. Both men remember being on the ship, but they both also remember never being out of their "here and now."
Does this work?