We should all agree that your problem is mositure wicking upward and its contaminating your drywall.
second, since the attic is soo cramped and hard to work in, I would suggest that you also pancake new rock over the old. Then you will have to work with the light and some other areas that I am sure molding will come into play.
I would suggest adding the Green Board to the ceiling and getting a light either with a fan or a light that is sealed and will eliminate vapor from getting into the light workings and then contaminate the rock around the light hole.
Then I would use a water proof compound and also fiber tape for the bedding work.
Then do your texturing, but would not recommend going back with popcorn. Then prime it then use a good quality paint dealer kitchen bath latex paint for just this application.
Forgot, I would use the primer suggested by the other person. sorry about that.
This will be an area that you will have to inspect and periodically paint more often that others to preserve the integrity of the ceiling anatomy.