I don't believe it's about a 'trust vs channeling strength' equation; it's about who Rand thinks would be most helpful at The Bore with a necessary element being trust, which is why I'm on the fence between a 1) Min, Nynaeve, Rand group, 2) a Moiraine, Nynaeve, Rand group and 3) an Egwene, Nynaeve, Rand group.

Honestly, I think some readers underestimate what role RJ meant for Egwene to play. I think Rand trusts Egwene in different ways compared to his trust for Nynaeve - he respects her in a way that he doesn't other characters in his retinue. Perhaps it's due to Egwene being a leader and other factors, such as being the first in the group to fight the Forsaken, knowing her importance to him during the Seanchan's first Return, etc. Maybe R.Jordan wasn't successful in painting an image of a strong woman that people would like, but he did try to show that all the other rulers respect her. The last book even had Rand concede that he expected nothing less from Egwene than to unify the Tower and become it's leader. As much as some people hate to admit it, every member of the principal cast is meant to be a hero or heroine.