I don't like the idea of the drywall anchors used. Gypsum panels (what ceilings are usually covered with) are just two sheets of cardboard with 1/2" of chalk between them. Any kind of humidity is going to severely weaken what little integrity there is. Not to mention that the gysum sheet itself, which weighs a ton, is only held in place with more-or-less tiny screw or nail heads, also holding only cardboard.
3/4" x 3" pine is not that light, especially if you use rockwool. I'd take the time to locate the joists in the ceiling and anchor the panel into those with 3/8" lag bolts or hooks (make sure you screw into the center of the joist). If the joists are not in the right spot you can screw a piece of plywood across them and anchor into that with T-nuts.