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.