Some of these points I have definite answers to, so I'll just confirm them now:

The rescuers WILL have their own network. (In a lot of ways its kind of like having traditional jamjar characters stumbling in on a memory loss/AU game.) Finding ways to contact the abductees will be challenging but is certainly on the list of things rescuers can focus on.

Kidnappees regaining enough agency to function as a double agent will definitely be possible, though obviously risky.