The more I think about it, the more I like this idea. We're due for another time travel film, but howabout, instead of traveling back to Earth's past, we travel back to the Kronos's past for a change?
The conflict is going badly, so some Marcus cohorts send a Red Matter bomb to blow up Kronos. Enterprise
tries to stop the injustice, but they fail and the still bomb detonates inside Klingon solar system and Enterprise
gets trapped in the vortex and sent back 1000 years.
is damaged but not too badly, however the dilithium sustained enough damage that only slower warps are possible. Spock theorizes that it may be possible to return to their time by slingshoting around the sun at maximum warp. Of course, they don't have near enough power to even think of trying.
Then Carol mentions a terraforming project she proposed when she studying at Cambridge. It was ridiculed for being romantic and idealistic, but mostly people thought it impractical because the amount of energy required for something like that was immeasurable.
However, one of the best candidates she found in her research was the mined ore Klingons extracted from Praxis. In it's natural state, it was still one of the most uncommon elements in the universe, however it was the way the Klingons artificially refined it into an isotope that made it so powerful (and unstable).
The refining process was still secret, however, the reason Klingons came to know of it in the first place was because bits of Praxis fell to the planet, and the isotope formed over eons of decay into a ruby-like rock the women of this era wore as gaudy jewelery.
So Kirk decides to go find some. While they're there, they discover the two main House factions are in the middle of a blood feud. But there is a third party advocating for peace and trying to play mediator.
Spock suggests that, if they help the third faction, they might alter Klingon way of thinking enough to change their bloody path over the next millenia to the point where there might not be a war.
The PD gets thrown around and Bones argues they have no business telling another culture its way of life is wrong. Spock points out, that the bomb likely destroyed Kronos much like the drill did Vulcan. If they were to leave things as is, they were likely to go back to find it gone. And since Klingons are even more indigenously clustered than Vulcans, that they may be even fewer of them left. If they alter Klingon philosophy enough to ripply through the centuries to stop the war would ultimately meant the preservation of the species.
So after some Klingon 300 battles, bat'leth twirling, and other bloody stuff, they get their hands on one of the Praxis rocks and are about to go home when Kirk ask Spock why he doesn't adjust their calculations and take them back to when Nero first attacked the Narada.
Spock says, saving the Klingons was an imminent problem they were indirectly responsible for. However, the new time line has altered the course of trillions throughout the galaxy. The effect of reverting the timeline, or even just saving Vulcan, could have a potentially catastrophic effect on an unimaginable number of lives. The old course of events had its time, it was best they forget about it and accept their new fate.