Well, our heroes do go to all the trouble of returning to the immediate past - something they wouldn't have to do if their aim was merely to get home. They apparently want to do something to prevent Christopher's jet from breaking apart - and I can see two ways of doing that.
1) Contact their past selves and tell them to hold the tractor beam. Not likely to work, due to poor communications and so forth. (But their past selves should by all accounts have been there in the sky somewhere, with two starships messing around. We could assume the ship that was deliberately timetraveling did not dip into the atmosphere, though.)
2) Distract Christopher long enough that he won't enter into the situation that makes the past Kirk order the tractor beam. The silly transporter-superimposition thing they did would have been perfect, I guess... But it would still result in the death of the originally captured Christopher, in cessation of all of his thought processes and memories and replacement thereof by this uncaptured one's thought processes and memories.
There would have been no reason to do anything to the uncaptured sergeant, but they needed to get rid of the captured one - so again this silly trickery might be a nice way to do what they had to do.
I'm sure it wasn't an easy decision for them. It may even be that not all of them realized what they were doing. But it does seem as if they are giving some sort of a performance for the two ancient Earthlings when they start babbling about this transporter superimposition stuff - they "catch on" one by one, and add convincing-sounding detail, until it sounds as if everything will be fine.