Thing is, what choice did Gawyn make that prevented Egwene from being killed? Leaving the Younglings? She wasn't in danger of being killed, especially with Elaida being carried off by the Seanchan, and Gawyn had to part in the that. No one else believed her to be a Darkfriend at that point. Gawyn may have helped mobilize/galvanize the rebels to move in, and while it may be true that that helped against the Seanchan, were Egwene re-captured by the Seanchan, again, she wouldn't have been killed. She'd have been leashed.

I wonder if the choice in question is when he decided to allow Siuan and Leane to escape with Min. Imagine what would have happened to Egwene as the figurehead Amyrlin without Siuan's and Leane's support and guidance. Imagine what she would have done had Siuan's Gawyn-enabled escape hadn't led Siuan to Gareth Brynn, which led to his eventual decision to side with Egwene's Aes Sedai?

Perhaps that was the decision. One question though, which is the lynchpin: when did Egwene have that vision of Gawyn? Pre-Siuan rescue or after? If after, then my theory doesn't work. If after, then perhaps it will be related to his (eventual) decision *not* to attack/kill Rand.