What I think happened was this:
Bryne had a plan.
He'd given the bare bones to Egwene, but hadn't elaborated on the specifics because hey, he still had months to iron out the detials and impliment them.
He'd already told her that he intended to use ships to blockade the harbours, but he hadn't told her that he intended to get the ships XX miles south.
Then Egwene declares that she intends to Travel to the Tower in 1 month - which she had kept incredibly secret because she didn't fully trust, well, most Aes Sedai, really.
So we have this situation where they know exactly which day they are leaving, and arriving, with none of the distance inbetween covered, and by the time Bryne can come in and tell Egwene that its buggered up his seige plans, there is little they can do, because its not like Egwene can go back and say "Never mind, my mistake, we're all going the normal way."
As for negotiating - I think all the important and influenctial people knew that negotiating would be a dead end and it was pointless to even try.
They know that Elaida is a megolomanic and wouldn't step down unless forced.
They had as little hope that the Tower Hall would meet their demands as well, though they at least will listen.
So on one side, negoitations are a known dead end, but on the other a direct fight will end in Aes Sedai blood being spilt, which must not happen.
So a Seige is the best position at the moment, because they can begin demanding thing.
And they have actually come up with a Plan B for the seige, though only a few people even know they needed one.
Which brings me to the next part in my updates -
The Aes Sedai have rediscovered caullander - cool, but it came out of fricken nowhere.
The only explanation we get is that Moghedain taught Egwene all she knew, and Egwene built upon it from there, but still.
Then we move onto the Hall meeting and finding out that in light of the giant Saidar beacon, 3 Sitters hve put forth the idea to enter into an alliance with the Black Tower.
I remember being very happy with this idea the first time I read it, and I'm still rather pleased.
I'm still surprised at the vehamance that some of the Sitters opposed it though.
They suggested the Sitter who proposed it was a Darkfriend.
What, do they think that every man who can channel = Darkfriend and evil?
Well, I'm pretty sure Taim, if not a Darkfriend, is at least a giant cock and plotting against Rand, but still.
In the end, they agree to the idea, but not on how to go about it, and spend the rest of the day arguing about it.
Then we move onto Egwene Dreaming, which has a couple of interesting things.
Mat is bowling, killing thousands, Egwene is climbing a mountain and a Seanchen woman saves her, offering to do the climb together, and the Seanchen are going to strike the WT.