The first two parts of my theory only work if Egwene is part of the circle with Rand and Callandor.

Egwene as Amyrlin must assume that Rand is going to break the world again during the final battle. After which the people of the world are going to be looking for leadership, and that leadership undoubtedly will be the White Tower.

When Egwene finds out that she needs to be in the Circle during the final battle, I think she'll realize that she needs to find a successor that everyone will stand behind in the event that Egwene were to be killed.

If she doesn't step down and she were to die then the Tower would be unstable when the world needs the White Tower to be at it's strongest. I think Egwene will choose Suian Sanche to be Amyrlin, and here's why...

1) Suian was deposed and stilled illegally.

2) While Egwene was held prisoner she met a very wise Aes Sedai who could barely channel, and thought how unfortunate that such a wise woman was over looked simply because she barely could channel.

3) Suian stepped up and took charge when the Seanchan attacked the Tower. She made the comment that Egwene may not be in as much control as she thinks just as Suian thought before she was stilled.

The other woman in the circle I believe will be Moirane. The women in the circle will need to be ones that Rand trusts, so if it isn't Egwene then it will probably be Nynaeve.

Finally onto RJ' final chapter:

I always thought that the Dream World was a perfect place to finish the story. Because you could have a big blood bath where all your favorites die,and then they can all get together again after the battle and wait to be woven out again.

Rand I believe is going to die, and be summoned back by the Horn of Valere. Afterwards, Rand/Lews goes back to the Dream World where he is reunited with Illeyna. This is where we find out which one of the women in the WOT was Illeyna all along.

I have two guesses on who that is:

1) Min. That would be the reason why Rand could never send her away because he knew unconsciously that she was Illeyna.

2) Egwene. They were born in the same village and meant for one another, but not in the way that he thought. Before the female Aes Sedai didn't support Lews Therins plan and that caused the taint, this time they support Rands/Lews plan essentially righting a wrong.