Egwene didn't say she will use hidden strings, or even bands of velvet or silk to bind the others, which would point to the meanings you saw.

But she used lace for the metaphor of what she hopes. Lace is delicate, complex and above all, full of holes... It's also not meant to be unseen, it's meant to attract attention, and like embroidery, be something to be proud of, to use with your best clothes...

Egwene was telling herself that she intends to tie the various groups to the Tower, but not to enslave them with bands of steel, to force them to become Aes Sedai. She rather intends ties that will please each group, and that will leave a lot of independance and freedom to each group. She doesn't want them to vanish into the Tower, she wants them to be what they are, but adorn themselves with delicate ties to a central organization of all channellers. The Aes Sedai, WO, Kin, Windfinders will still be seen underneath.

Tuon used a similar symbolism when going under the veil. She hid her baldness under a lace cap and sheer veil. It hid nothing of what she really was underneath, or changed her real nature. It was merely a symbol, to tell her court to treat her as a High Lady, because she considered she couldn't asked her court to treat her like the heir, when she had to atone for faults to be deserving of such treatment and honours again. Tuon thought she had let the mortal woman Tuon and her emotions rule her behaviour, that she wasn't fit for the station of DOTNM until she had atoned for that.

Egwene doesn't know it, but she's aiming to transform the Tower back to something close to what the Hall of Servants of the Aes Sedai Guild used to be before the breaking: a federative organization of all channellers from around the world. There used to be small Halls of the Servants in every locality. The Guild was more an organization to train channellers to their fullest potential, to organize their services, call and dispatch AS where they were needed and regulate proper, ethical use of the One Power. The Guild as Mesaana alluded to used to be a sea of fluctuating factions held together by the central Hall and a common ethical code. Not all AS by a long shot were working in the Guild like LTT or Bel Medar. A great deal of them, the vast majority most likely, lived and had careers outside the Guild. Being AS for many was like being a volunteer fireman: if your local Hall or the higher hierarchy called for your services, you were bound to provide the services, as a Servant of All. Elayne is already working at the recreation of aspects of this, with her ideas for the Kin. Egwene on her side is beginning to see how the administrative and political aspects could work.

The LB aside, this needs to be achieved - and soon Egwene will have to realize it must include the men as well (I get the feeling Rand is soon to bring this up... that he wants her to welcome his Asha'man back as Aes Sedai... He used to see himself more as an Asha'man, the first of them. Now, he's reclaimed his rightful title of Aes Sedai. He sees his mistake of seing these men as weapons aimed at the Shadow, not as human beings. He owes them something to redeem what he's made of these men. I think he will do it by insuring their future, back into Egwene's alliance of channellers. Some of the channelling factions are already planning to go to war with one another post TG (or in the case of the Seanchan, right now!). - a central organization, to prevent this, is desperately necessary. The Tower conflict was a necessity - the Aes Sedai,especially Egwene, had to see and experience the perils of factions, even inside the Tower, to understand how they must change their views.