Take that piece out and put it on top of a scrap piece of new drywall. Trace it with a pencil, and cut it out with a knife just a hair smaller than the piece you cut out.
The goal is to have the patch fool your eye into not knowing that there is a bulge in the middle of the wall. That is the entire premise of taping a room as well... filling in the bevels, and building out the butt ends of the drywall. Fool the eye. And the more your build it out, and the smoother you sand the outside edge, the better you will fool your eye. Finish taping, and mix up a small amount of the Easysand '5.' It is 2 parts powder to 1 part hot water. The hot water sets faster, and you can put more coats on in less time, but you have less time to work with it. Make about 2 golfballs worth.
If you hold the right side of the blade against the wall, and hold the other end up about a 16th of an inch, it makes a nice smooth transition.
With coats 2, 3 and 4 go out another few inches with each coat, making sure the outside edge is as smooth as you can get it. Keep the middle as smooth as you can. Don't over work it. The smoother you get it, the less sanding. Ideally, the sanding is very minimal, and only at the end when it is dry.
Ok Go make a sammitch and wait for it to completely dry. Get a hair dryer and, moving it frequently you can get it to dry faster.