Let's assume that the latter is true, because it is the theory with the most evidence found in external texts. How is it they seek to accomplish this? Their biggest step forward is to weaken or destroy Talos, which they believe will weaken Lorkhan and free Akatosh. Thus, Time will no longer flow in cycles but will flow ever forward. Talos is especially key to their plans, as Talos has fortified the mortal plane.
In another thread, there was mentioned the possibility that, after defeating Alduin, Alduin no longer can bring about the end as written; instead, that task will fall to a replacement. The Dragonborn is mantling Talos to be sure, but is devouring dragon souls at an alarming rate. It's possible that it could fuel an insatiable hunger that would lead, essentially, to the creation of a new Alduin. Thus, Shor becomes Talos becomes Alduin.
Here's the question: Are the Thalmor doing this intentionally? If they remove one Talos to be replaced by another, what does that do to Akatosh? Are the Thalmor aware of the kalpa cycle?
I suspect that they are aware of the kalpa cycle, given the mention of Akatosh as the "Free Serpent" should their goals be met. The best way to make a universe receptive to escape or reshaping according to their terms is to make time flow forward endlessly. Alduin's sudden appearance was a massive wrench thrown into that plan, with the Dragonborn causing further harm. It would explain their desperate and frantic attempt to gather anything they could on the return of the dragons. The fact that they were essentially sitting ducks in the Embassy if a raging dragon decided it wanted elves for a snack. The conversation between the guards in the Embassy confirms this.
Ultimately what I'm getting at is that the Thalmor seek to free Akatosh by destroying Talos. If Akatosh is freed, and Talos is reborn through the Dragonborn, then we get an endless kalpa in a world forever fortified by a mortal made into a god.