I'll respond to the rest of your quote at a later time, but the compulsion thing is simply a matter of statistics.

Sure, she knew a sister who used a logical metaphor for serving Rand. Sure, she herself knew the influence of his ta'veren nature. Sure, she knew there would be some untrustworthy sisters who might swear fealty to him to get close to him and then betray him.

The problem comes when more than 30 sisters, from different factions, all find some reason to swear fealty to him, over time. Ta'veren doesn't work like that. Egwene doesn't even know there was a time when both Tower and Rebel emissaries were in the same place at once (Dumai's Wells), and even then Rand's ta'veren only affected the Rebel sisters.

Egwene is absolutely right to suspect Compulsion. What's more, she was perfectly right. The only thing is, Rand wasn't the one doing the Compulsion, it was Verin. And secret Light-sider within the Black Ajah is a little out there, as theories go. From a distance, the sisters certainly looked like a bunch of people who were Compelled, and the simplest explanation was Rand, since he stood to gain from it, and had potential access to them to do the compelling.

But Egwene doesn't outright blame him. She specifically says that even the thought of Rand knowing the weave is something she doesn't want. But she is very clear in never stating definitively that he did, just that she needs to consider the possibility and use it however she may.

In KoD, once she DOES learn of Dumai's Wells and the kidnap, she has a brief thought about the possibility of it being ta'veren, and that's the last we see of her wondering about the means by which sisters came to swear to Rand.

Put simply, this is far from the kind of paranoid certainty of Rand using Compulsion that I would expect if Egwene were forced to distrust him. It sounds more like someone forcing herself to face the facts over what the evidence shows. And let me repeat again: she was absolutely right, as was Siuan. It WAS Compulsion that resulted in both Rebels and Tower loyalists swearing fealty to Rand.