You know that this is a result of the move. The ceiling rafters could have racked or twisted and the dry wall has come loose.
Also, I have heard of people installing too much insulation and not thinking of weight causing the ceilings to bow and begin to release.
I am not sure about this, but others more knowledgable might jump in on this, but, you could get a screw gun and some 1 1/4 drywall screws and re screw the drywall panels back to the studs. Screw in and slightly indent the screws to sink in to the skin without breaking it.
then spackle over the holes.
Check out in the attic in the areas, being careful not to put your weight on the affected rafters and see if there is some sort of foreign thing that has fallen in that area to cause the drywall to bow.
If the actual ceiling joists are bowed in or bowed into the floor below, you can lay some 2x6 along the ceiling joists in the attic. then screw the 2x6 into all the floor joists. Then screwing the 2x6 to the bowed joists, might suck it up to the height of the others. Place the long 2x6 with the affected joists in the middle of the 2x6.