What can be done to stop the noise permanently? Replace the ceiling drywall?
The biggest problem is finding where it is coming from.
It isn't the drywall that is doing this. It is part of the framing that is moving back and forth under pressure. Usually a stud or something that want nailed good. They can move about 1/8 to 1/4" with each expansion and contraction. This causes anything from a small squeak to a solid pop as it finally overcomes the friction against the other piece of wood.
One moment and I will draw you an example.
If we were to attempt to address the problem, is it big bucks to adjust if we can locate the spots with the issue?
That I cant say. it might be a simple matter of adding a few nails, or it could mean taking off a lot of drywall and then trimming the framing to allow for a little movement of the structure.
Below is an (simplified) example of one I repaired a long time ago. It was in a basement that had not been drywalled yet. It was a matter of trimming the framing back 3/8" to allow the beam to expand and contract without sliding on the plate.
Is that considered a big project, to do what you did? And how much was that particular project? Just trying to figure if addressing issue may be worth it. Thanks, XXXXX XXXXX very helpful.