Here is a little trick that may help simplify your project.
To gain access mark a line horizontal slightly above your required access point.
Use a sheetrock "stab saw" and cut horizontal until you contact the stud.
From the original starting point, now cut horizontal in the opposite direction until you contact the next stud.
Cut vertically down both sides maintaining contact with the stud as you go, until you reach the required depth.
Now cut horizontal across the bottom and carefully take the piece of sheet rock out, and set it aside.
After you have made your repairs, you can screw in a couple pieces of 2 x 4 on the inside of the studs, and the piece of sheetrock you removed will fit back in for and exact fit.
screw the sheetrock in place, mud and tape, and paint.