Verin didn't need to be a member of the SC to work to identify sisters, but she's pretty old and given her other goals (of learning as much as she could of the DO's plans, from the Forsaken etc.), it's a position she would have made everything she could to obtain, and given how many times she was involved without raising suspicion (from Alviarin), I suspect she was very high ranking indeed. Next to Galina in rank is certainly a possibility, she seemed to know Alviarin was the leader of the SC. Alviarin brought her to Fal Dara where she's the BA who got close to Siuan/Moiraine there, she was the one who disappeared to tail Rand, who brought back the Horn to the WT, who let the BA know about Siuan's hunt, she was let again be in Rand's entourage (and decided at a crucial point she had to disappear, it speaks of her being known to the Forsaken and their spy etc.). That she was Alviarin's most trusted agent and one of the two women she could speak to openly as leader of the SC would make a lot of sense. More sense than if Verin is only a rank-and-file who gets written orders but seems to meddle of her own initiative a whole lot. In her scene with Egwene, Verin alludes to a debate about letting her or not give notes to Egwene about the 13 BA who went to Tear, and deciding she had no choice. I'm pretty sure the SC doesn't debate things with rank-and-file, that this was a debate among the SC Verin was part of.

I think we've seen the SC in action on screen only once in the series (well that and their capture of Tamra, but for this we know only Galina was involved, and the Tower Coup where we saw mostly Alviarin/Sheriam/Galina), and it's in the debate about dwindling that went on for years - the top dividing debate among AS - where they appeared to work in coordination.... three women we know were involved personally where Alviarin, Verin and Sheriam.. and unknown Reds with whom Sheriam was nearly coming to shouting matches. The whole ploy would have been far easier to organize among SC members than by messages sent by rank-and-file.

For Sheriam it's an implication she made in her POV that she strived for a high rank by ambition. Her strength, her key position, the fact she remained mostly in the WT, had the trust and friendship of the Amyrlin and the fact she was a very high ranking Blue would make her a likely candidate to enter the council. In the Tower Coup, Sheriam played a key role, pretending to fight, and organizing the escape of many novices and most of the Accepted. She was likely still a junior member, but I think she's one of those BA who knew a lot of the actual plans (most of the rank-and-file BA don't seem to have known much about what truly happened with the Tower Coup).

As for the meetings, I don't debate the fact they could narrow down and puzzle out who the members were based on strength, I just find it fairly obvious RJ would not have overlooked this and maniacal about such details as he was, he no doubt conceived of a trick they used. It would be more profitable to discuss how they possibly did that then debate whether this was a huge mistake by RJ (which seems to be your point).

Brandon pretty much deprived us of whatever "BA resolution" RJ had in mind to offer by failing to continue Alviarin's storyline. For a few books, RJ was starting to reveal internal details about the BA, knowing their downfall was coming and how. At the end, Alviarin was on to Talene and the hunters, and getting close to Egwene. She appeared in a chapter written or outlined by RJ, then nothing. We'll probably have to wait for the Encyclopedia to discover many of the details concerning the organization that RJ could have used in Alviarin's last pre-purge POVs. RJ'S method to start with the core then work outward by adding layers seems to have disserved us with Egwene's storyline, especially with the BA hunt. We got the core more or less intact, without the missing layers (counter POV and so on) RJ would have worked on at a later stage.