Honourable mention for Saerin 🙂

But Mat had made a promise to Rand to see Elayne to Caemlyn, so if they'd managed to dodge him, he would have taken the Band right after her which again puts her in the position of looking like she's taking aid from the Dragon. The girls specifically talk about how dogged Mat is in his promises, so then the Band wouldn't have been around for Egwene to use in her manipulations. Elayne was frequently mentioned as the expert on ter'angrael, so she was needed as the most likely to figure out how to make the Bowl work. They didn't start off with the plan to involve the Sea Folk, so it would have been on her to figure out the workings as the Aes Sedai who also has some experience in Weaving the Winds on a Sea Folk level. Who would you have sent with Nynaeve and why?

But also wasn't Elayne's whole thing that she didn't want to be seen to be 'accepting' the Lion Throne from Rand? Which is what being escorted by the Band (seen by most as Dragonsworn) would have done. And in the end a lot of her support came from Dyelin, who admitted that she wouldn't have supported Elayne if she had accepted the Throne from Rand rather than by taking it in her own right. Even if she tried staking her own claim after arriving, the fact that her arrival would have been facilitated by Rand would have made it harder for people to accept that she was being independent. Not to mention that Nynaeve couldn't reliably channel at the time they were sent to Ebou Dar, so sending her on her own would have been silly. Egwene did not have many true allies at that point, and the Bowl was one of the most important things in the scope of the world at the time, so of course she'd send her two most trusted allies after it.

Do we know if Galad always had the Damodred name, or did he start off as a Mantear? Because with Tigraine being the daughter-heir and presumed next Queen of Andor, I would imagine he should have had his mother's surname, just as Gawyn and Elayne were Trakands. He would never have been in line for the Lion Throne, but he would have been presumed First Prince of the Sword for whatever sister he wound up having, so again you'd want them having the same surname. Was he taken out of House Mantear when Modrellen died and Trakand became the ruling House? I know Taringail always wanted his son on the Sun Throne, but how would that have worked with him being First Prince of the Sword? Or do we just assume there was a deal that the first son would be a Damodred, but the rest of the children Mantears?