Did you really only read up to the bit about squashing resistance and skip the part where I explained exactly why?
Anna never worked for Lilith. Ever. I knew her, intimately in fact, and she rebelled against heaven but never worked for Lilith.
If you're so knowledgeable about the Cage, why didn't you stop it opening in the first place?
The fairies claim they can find the back door to any prison. three problems with that: One, it's a claim that has never been proven. Two: the Cage isn't like any other prison. Three: even if they can, and even if they can get in and out of the Cage at will, they wouldn't be able to take anyone not of their folk with them.