The reason behind Cyndane's reduced strength will not be related to Healing/Stilling or a problem with her new body. It won't be something as mundane as that.

Instead, it will clearly be something plot related. Cyndane's weaker strength isn't simply a by-product of some unfortunate accident - her reduced power is central to the plot itself, else it would not have needed to remain secret for so long.

The Stilling/Healing idea is just too ordinary and anticlimactic.

And the fact that BS was only "85% sure" that strength is tied to the body shows that this cannot be the reason behind Cyndane's weakened state. BS KNOWS why Cyndane is weaker, and if it was due to her new body, he would have known with 100% certainty that strength is tied to the body. Besides, this has no plot significance.

No, the reason for Cyndane's weaker strength is something that had to remain a secret up to now, and which will be revealed in the next book, according to BS. And we know that in the next book it just so happens that Moiraine will be rescued.

And it is at this point that I believe we will see that Moiraine has GAINED strength. And I believe we will in fact find out that Moiraine has GAINED exactly as much strength as Lanfear had lost.

I believe this will allow Moiraine to reach a strength level above Cadsuane, and thus gain a higher level of seniority than Cadsuane. Moiraine will take Cadsuane's place as Rand's advisor, and in this way he will once again trust Aes Sedai advice.

So the crux of my theory is that Moiraine and Lanfear somehow exchanged some of their Power when going through the doorway.