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.
If Egwene doesn't know so many of those details, how does she know about more than 30, from different factions? It didn't affect the Tower sisters as far as we know, because he didn't ask anything of them. There is no reason to suppose it would not also affect the Tower sisters, or that it would not work on more than one occasion.
Since it was true, and the subject of fan theories going back decades, it is not so out there as the idea of Rand raping multiple women. The point of this is not being wrong on Compulsion, but Egwene thinking it of Rand. She might have thought someone else might do it, but that Rand would order it or allow it, much less the Wise Ones is worse than absurd. But she has no problem going there.
She doesn't think "someone is up to something to cause uncharacteristic behavior among the sisters," but "RAND is using the most vile means imaginable of coopting sisters." What is more, the uncharacteristic behavior that absolutely cements in her mind that these women MUST be compelled, because they would NEVER go along with this otherwise, is negotiating an end to a rebellion against the Dragon Reborn. If Egwene is right at this being unthinkable behavior without Compulsion, that says something much worse about the Aes Sedai, and nothing good about her that she would defend them against Rand.
Because she doesn't want him to know or do anything. She is appalled at even innocuous things like restoring the fountains of Rhuidean or creating stedding.
But not Rand doing it. And she was also making that assumption based on the aid given him by women who were not even Compelled. Even strangers realized after a few weeks of observation that Rand was incapable of harming a woman. But someone who has grown up with him can assume he can do the worst thing possible, short of murder, based on second-hand reports in a series that is constantly drumming home the point that the truth gets further lost the more hands it passes through?
“Tolerance is the virtue of the man without convictions.” GK Chesteron
Inde muagdhe Aes Sedai misain ye!
Deus Vult!
*MySmiley*