...but I'm not sure I can agree with your conclusion. As others have mentioned, being so much in the spotlights as Head of the Red Ajah requires a skill to mimic someone else I think few people have. It's not a coincidence most forsaken choose to hide as an unexisting person rather than take someone's place. It's simply much easier.

Finally, remember the hint dropped in earlier books about a flash of Mesaana's real dress appearing under the mask of mirrors? Someone made a list of Aes Sedai who were known to be wearing a similar dress. IIRC, Tsutama wasn't one of them.