So, we've got the crew of the Enterprise in a Klingon Bird of Prey. The planet Earth is being attacked by a probe that wants to talk to whales. And the crew are going to attempt time travel.
If I was Kirk, I would have pulled Spock aside and said:
'You know, we've got a chance here to make a difference. Why don't we try to get back a couple of stardates sooner, send a subspace message to the Reliant and tell Capt. Terrell and Chekov not to beam down to Ceti Alpha 5 and to put up a damn warning beacon like we should have to begin with. Khan won't escape the planet, the Reliant crew won't get stranded, Scotty's nephew would still be alive, the scientists on Regula 1 won't get slaughtered, you won't die from radiation, the Genesis Device won't get detonated and the Genesis planet won't become a galactic controversy, so the Kilingons won't cross the Neutral Zone and kill my son, and we can get the whales to Earth before the probe even shows up so it will turn around and go back to wherever.
I think it's a win, win.'

If I was Kirk, I would have pulled Spock aside and said:
'You know, we've got a chance here to make a difference. Why don't we try to get back a couple of stardates sooner, send a subspace message to the Reliant and tell Capt. Terrell and Chekov not to beam down to Ceti Alpha 5 and to put up a damn warning beacon like we should have to begin with. Khan won't escape the planet, the Reliant crew won't get stranded, Scotty's nephew would still be alive, the scientists on Regula 1 won't get slaughtered, you won't die from radiation, the Genesis Device won't get detonated and the Genesis planet won't become a galactic controversy, so the Kilingons won't cross the Neutral Zone and kill my son, and we can get the whales to Earth before the probe even shows up so it will turn around and go back to wherever.
I think it's a win, win.'
