no need to tear a hole that large. Even if you go out to the studs,
you still have the 'floating' section between.
Rather, use some 'paper' boards 1/2 inch thick by 2 to 4 inch wide.
The paper is super easy to cut to length - use a matting knife. use
four pieces to 'frame' the hole. Mark center lines along the length of
the boards, then placed arrow heads across the CL, because when in the
hole you can't see the boards anymore [when the BOARD is in the hole]
Reach inside the hole hold the board with one hand, then sheet rock
screw the boards to the inside of the hole through the surrounding
drywall. Four places, completely frame the hole. Then even a poorly
cut drywall plug will insert and fit over the frame, and screw that
into place. What you end up with is a very strong contiguous strength
drywall sheet that cannot crack out even as the wall flexes with age.
I used this technique to 'pull' into place two running sheets in the
ceiling that were causing me fits with both not lining up and thus
cracking every month.