1. Strapped Ceilings Attach the air barrier material to the underside of the ceiling joists or trusses. Strap the ceiling beneath the air barrier with ripped 2x4 or 2x6 material, fastened with structural screws. Then cross-strap with 1x3 strapping. Fasten the wiring to the sides of the 2x strapping, tight to the ceiling, and fasten the drywall to the 1x3 strapping. Be careful not to poke holes in the air barrier.
2. Hallway Plenums Attach the air barrier material to the underside of the ceiling framing. Frame a dropped ceiling with 2x4s, running from wall to wall. This creates a chase large enough to contain ductwork, wiring, plumbing, or even a small air handler and indoor coil for a mini-split heating and cooling unit, keeping all that equipment out of the insulated attic.
3. Strapped Walls Apply a smart vapor control membrane to the face of the stud wall. Strap the walls with 2x4 material or ripped 2x6 stock, run horizontally. This creates chases for wiring inboard of the air and vapor control membrane. If you need more room, you can frame a whole second wall inboard of the air barrier.
4. Baseboard Raceways Here's a trick to provide an isolated wiring chase without having to fur out the whole wall: build a raceway into the space behind baseboard molding. In a more formal room, wainscot wall paneling can be installed similarly, with an air space that provides lots of room for wiring. Either way, apple the air and vapor control layer membrane to the wall before furring out.