... except of course there's a heavy suspicion that Aviendha's vision was either just a possible future, or that the programming of the ter'angreal has been tampered with since the Forsaken could access Rhuidean once the shield was no longer there.

Aviendha's vision can be summarized as: following Rand and his plans lead to your extinction by the Seanchan even if he wins the LB. That put pressure on the Aiel, and it's lucky this vision was seen by Aviendha and not a WO already doubting Rand.

That's not enough to prove the Shadow has touched the programming of that ter'angreal, but it's not impossible to discount it either, not when the Forsaken have gotten free access to it since the shield in Rhuidean in gone.

Of course Rand will serve the Seanchan as he serves everyone else: as the Creator's champion. I can imagine performing some little act of humility/apology, but I seriously doubt he will bend knee in the sense the Seanchan understand it any time soon.

The only way this could happen is if Rand decides to announce officially (he's already said it to his inner circle) that he isn't meant to lead the world, that his role is to fight the Shadow as the Servant of All and he symbolically bends knee to the world, and thus that includes the Crystal Throne. Otherwise, Rand bending knee to Fortuona alone would amount to legitimizing her claim of political hegemony, and alienate all the other rulers Rand doesn't bend knee to.

As for the "binding the Nine Moons" to him, there are two main ways to see it. The first is that it refers to the Seanchan High Blood and Imperial line, who are the courtisans of the Empress. Those courtisans and the physical location itself are called the Court of the Nine Moons. The second way to interpret it is that it was referring to the Daughter of the Nine Moons, and thus to Tuon, not to Fortuona the Empress, and that gives us a timeline.... The propheciezed binding thus already occured by Tuon's wedding to Mat (he joined the Court of the Nine Moons as Prince of Ravens), we just haven't seen yet how Mat's wedding will eventually bring the Seanchan behind the rest of the Light, except we know he's now returning to Ebou Dar to meet his wife.