The test of how effectively Elspeth is hidden is how people other than Allirea react to her. Saeed lets her out of the cell, which constitutes excellent evidence that she can fade well enough to get the job done.

Yes, this tells that changing lies work. This doesn't address the question of efficacy of muttering the same lie.

Also, that "I'm 51, I'm 52, ..." works is indirect evidence that constant lies work as well, and proof-of-concept of how figuring out an efficient low-creativity algorithm can indeed bear fruit.

When Allirea fades someone else, Allirea herself is not affected by this.

She noticed that Elspeth "announces her presence" loudly, which is a perception on the same scale.