One way to handle this if possible would be to measure and locate the exact placement from the attic, marking the joists where they are to be cut, and again where the added 1-1/2" frame will be. Then use an awl or small drill bit (just the bit-no drill) or even a small screwdriver, and put holes down through the drywall at what will be the inside corners once the frame is installed. Now, from below, you have each corner located and can cut away only the drywall you need. You do have to do some careful hand-cutting to remove the last of the joist ends at the drywall, but having the opening there helps a lot. An alternative if you will have a trim frame that will cover 1-1/2", you can use a reciprocal saw through a slot in the drywall at the base of each joist end to finish them off.
One more method is to cut the drywall flush with the joist cutbacks, and use a larger board for you frame (if joists are 2X6, use a 2X8 frame), bringing it down 1/2" lower, so that the bottom is flush with the ceiling side of the drywall, then you have a nice, solid edge to attach a trim frame to.
Any of these methods will work; it's just a matter of which you like best. Good luck