Seems pretty obvious to me.
The Changelings extracted the part of Picard's brain affected by Irumodic Syndrome. Not so they could use the Irumodic Syndrome bits but so they could make Picard's corpse occupy-able by something.
The same something that's hitchhiking in Jack.
That something being a Pah-Wraith.
So that a Pah-Wraith can walk around in Picard's corpse, impersonating Picard, during the ceremonies on Frontier Day.
The female voice saying, "Find me" is pretty easy to identify as Nana Visitor's voice. Obviously she's not playing a Pah-Wraith. Kira is somehow the one who closed the red door -- or a Prophet in the form of Kira is, which now that I think about it makes more sense.
Which means two more old timer appearances:
Nana Visitor portraying a Prophet, and either Avery Brooks or Cirroc Lofton as Sisko / "The Emissary".
There. Now, I feel confident in saying that this post won't spoil anything for anybody, since most of y'all consider me to be wrong on every topic by default.