Frame coffers in my ceiling for new remodel

I have torn the walls down to studs in an old 1910 house and replaced the plaster and lathe with new drywall. At the same time I opened up the floor plan and installed some new headers. To hide these headers I am going to install new coffered ceilings and that requires traming in some 16" square coffers around the perimeter of the room.

These coffers will hide recessed lights for highlighting artwork, a projector and motorized screen for the home theater and HVAC for the upstairs.