My theory is that Egwene is successful in convincing enough people to stop Rand that he has to go to the Seanchan for help. I think that in demand for female channelers to assist Rand in resealing the bore that in return Tuon demands that Rand submit to her authority, e.g. publicly acknowledge her and bow before her (that sort of thing). In addition, I think Rand demands the Seanchan covenant not to attack further nations in the Westlands and demands that the Seanchan not take female channelers except in the lands they already occupy now.

Then Rand, with the help of Seanchan female channelers, defeats the Dark One, saving humankind. This also happens to fulfill Egwene's dream of being rescued by a Seanchan. If the Seanchan hadn't helped Rand nobody would have beaten the DO and Egwene would end up dead. Thus, the Seanchan saved her (and the rest of the world). At some point after the DO is resealed, the White Tower and the rest of the world come to the knowledge that they almost caused the destruction of the world by opposing Rand's plan and supporting Egwene. They are all thankful to the Seanchan and this is enough for them to support the peace that Rand negotiated with the Seanchan.