That's my feeling as well.
I was thinking all day about this at work, and now I'm not convinced the Green Man told her to bring the Dragon Reborn back to the Eye. It's been a couple years since my last re-read, but I believe they weren't heading for the Eye at all. Moiraine was trying to take...
“Will we reach the Eye today, Moiraine Sedai?” Egwene asked.
The Aes Sedai gave Loial a sidelong look. “I hope that we will. When I found it before, it was just the other side of the mountains, at the foot of the high passes.”
“He says it moves,” Mat said, nodding at Loial. “What if it isn’t...