Whether each does so quickly enough to suit Moiraine, however, is another matter, so you may be right about her absence from Ebou Dar. Still, ALL roads lead to Rand now, including Mats; he and Moiraine could as easily go to Ebou Dar together after a reunion with Rand as before one. The biggest problem with that is neither Moiraine nor Rand will want her out of his sight (or vice versa) once they are rejoined, but then, the Seanchan prophecies contend Rand has another rendezvous of his own scheduled with Tuon. Mat going to Ebou Dar is not so surprising; I doubt he wants to leave his blushing bride on her own long knowing the Last Battle is imminent (arguably already begun,) particularly given that intrigue and assassination is to Seanchan what baseball is to the US.

With or without Moiraine alongside, it is hard to imagine Mat letting things lie with the damane just because he is Prince of Ravens now. That would be like William Lloyd Garrison moving into the Confederate White House: Simply implausible. Too much of Mats plotline for the entire last half of the series has involved rescuing Aes Sedai from various unpleasant imprisonments, spending a lot more time than he would like getting up close and personal with them, and doing the same with sul'dam. This is clearly a case of an author Building to Something.

Much of that has involved Turon as well, and I do not understand why so many think her dismissing her channeling ability on the grounds ability does not equal action ended the matter. If adam really are just involuntarily links, everyone on BOTH ends is already channeling whether they know it or not. Once that realization percolates through Tuons rigid mind, it is all over, since it has been well established from TWoTs opening pages that channeling is more addictive than crack. Even if the Ever Victorious Army did not need channelers as its heavy artillery, Tuon could no more STOP channeling (either through damane or directly) than anyone else can. Likewise, discipline and honor or no, I cannot imagine her renouncing the throne and declaring herself a rabid animal to be chained (particularly since, as the last of her house, abdication would initiate a civil war she desperately wants to prevent.)