First, batt insulation is not to be installed over loose blown insulation because it smashes the air out of the spaces between the fibers, so the batts totally negate any effect of the loose insulation. Loose insulation can be applied over the batts but not the other way around.
Second, I suspect high humidity in the space above your drywall ceilings which acts to soften the ceiling gypsum drywall, therefore allowing and causing the sag.
Investigate venting your attic above this drywall ceiling to 1.5% of the total ceiling area. If your ceiling is 1,000 square feet of area then the total attic ventilation needs to be 15 square feet of vents, ridge vents, soffit vents or some sort of hole in the attic space to allow air to circulate in and out of the attic.
Third, the ceiling gypsum drywall probably needs to be 5/8″ thick fire code or Type X drywall for rigidity. This Type X drywall has fiber reinforcing inside the gypsum for strength and acts to keep the drywall rigid like plywood. The 5/8″ material stays flat when applied over a wavy ceiling and tends to visually flatten the sags.
Fourth, the rough texture ceiling residue needs to be covered with another drywall surface. See #3, above.
Ah … the joys and tricks of renovation.