The big piece of evidence is "The List of Names". Each time a woman dies on his watch, he adds their name to a running list in his head. At Dumais Wells he spent hours to days combing the dead to make sure no Far Deries Mai was forgotten. Over time the list grows to include everyone he failed...
All of the timelines we see in novel begin at Winternight. My premise is along the lines that instead of all the hunting Moiraine needed to do in "New Spring", she knew all along to follow Tam back to the Two Rivers.
In that moment, Egwene has become "other". They've been away from each other...
So my mind got wandering, as it does, and I wondered, would Rand have learned the final lesson in book 14 earlier and been better prepared for his trials if Moiraine or a similarly sympathetic Aes Sedi lived in the village. My inclination is that the sister in question would have been able to...