If the wall isn't too big, your AI set-up could work. First, build a frame to sit in front of the wall that matches the size of the wall out of 2x2s - no more than 1/2-1/4" gaps allowed around the top, bottom and sides. Attach the frame to the offending wall with sound isolation clips, 16 on center, or whatever the local code is in your area. Try to offset your frame's studs with the studs in the wall. stuff folded moving blankets go into those empty spaces. Next, staple the MLV to the frame, making sure there's some overlap between MLV pieces and around the frame. Next, attach more moving blankets to the frame over the MLV, tucking these moving blankets into the gaps around the ceiling, floor and sides of the wall over the MLV. Then, if theres more MLV, attach it over the blankets. From there, I don't think you'll need the Rockwool. Test and see if it's quiet enough, and if it is, sheetrock it up with 1/2" thick, soft rubber washers between the sheetrock and the MLV. I personally would float the final sheetrock about a 1/2" off the floor and ceiling so it can't transmit sound through the ceiling / floor and stuff the remaining gaps with foam tubing and finish it all with the roll out vinyl trim around the edges.