John,
I disagree for the need of a CBU on the ceiling of this shower.
You can do;
A) Leave as is as.
or
C) Tile over existing drywall, with or without liquid membrane.
If you simply paint it, I recommend using a paint made for this purpose. Use Perma-White by Zinsser.
Mold Mildew Resistant Paint - PERMA-WHITE Mildew-Proof* Bathroom Paint Jaz