Okay, here's a rough drawing:
Note that this is an overhead view, the room is toward the bottom, and the floating rectangle is the section of drywall removed for access, and to be reinstalled.
I'd suggest that six screws per sistered stud are plenty: two at the top, two at the bottom, and two near the middle. Two in each place so the sistered pieces can't twist.
Plus, I just noticed that the second and fourth screws pointing up should be shifted to the right a bit, so they engage the studs and the 2x4s.