I'm not so sure Egwene and Mat "don't work". Sure, it isn't a peaceful relationship like Egwene-Perrin, which is a potential goldmine of good ideas and good leadership, but it isn't all that bad either. Egwene is the one Mat came to for advice when he was worried in tSR, and that set him down the path of Rhuidean and all the rest. Mat respects Egwene's abilities, and bows to her to support her when she is down, surrounded by Sitters who see her as a puppet.

And in every conversation among the wondergirls about Mat, it is Egwene who's always saying, "Yes, he's a lout, but...". I'm not saying they're a perfect team, but nor do I think they need a mediator between them. Though I'd love to see Egwene's reaction when Mat tells her he's married to a sul'dam Empress of the Seanchan.

One way or another, though, I always got the feeling that Egwene's disapproval of Mat was more because it was expected of her than because she genuinely disapproved. Plus, the two of them have probably spent the most time with each other, since they both lived in the village proper, and Egwene's best friend was Mat's sister. They show signs of knowing each other very well, and there seems to be a quiet sense of camaraderie.

Longer replies to the other posts will have to wait, but I agree very much on your points about Rand and Egwene having to meet each other halfway, and neither being completely right, and neither taking a complete political fall. And I think the greatest moderator between Egwene and Rand will be Moiraine. She is one woman they both greatly respect, and she was the first mentor figure for both of them (well, Lan for Rand too, but Lan doesn't have the advanatage of being thought dead, and returning at the darkest hour). I even suspect that Rand needing a woman dead and gone has to do with this. Moiraine will have to play mediator.