There's a difference between suspecting an inevitable betrayal and having objective proof that the betrayal has technically already happened.
The dossier on Ulfric Stormclaok not only implied that the Thalmor have manipulated Ulfric into starting the war but that the Thalmor are actively prolonging to extended the stalemate and weaken the empire.
Since neither the Empire nor the Stormclaocks want anything that benefits the Thalmor to happen, providing said proof to them both at the same time is likely to get them on the same page and more open to the possibility of a genuine peaceful resolution that doesn't leave the EMpire weak or Skyrim vulnerable and gets the damned Thalmor our of Skyrim.
If the Imperials win, Elesif as the last Highkings's widow who already lives in the capital is almost certain to achieve the throne, and the implication is very much that only the Jarls are in the running.
You are at most a war hero, and there'd no way in the main game to marry Elesif or any of the Jarls and thus find yourself in a position to ascend to the throne.
Not unless you actively campaign from it... And since he Dragonborn has quietly been a good servant who just kind of stumbles into positions power, they have no reason to listen to you if you're campaigning to become the new king.
a conquest option would be something along the lines of not siding with either faction, probably via doing something with Balgriff since he only sides with the Imperials when Ulfric forces his hand, and then doing quests that involve driving both the Imperial army and the Stormclaokcs away from hold capitals and getting the Jarls who are currently in place to side with you ending with you defeating Ulfric or Tullius or both and that determining whether Skyrim uner your rule stays with the Empire or dlecares indipendance.