cut your square clean hole for access. Then on the inside of the square, screw some one by fours all the way around. This will stop the patch or trap door from going in the hole and keep it flush with the existing wall.
Now, cut a piece of plywood the same size as the hole and the same thickness of the existing wall board. You may cut the plug one sixteenth smaller all the way around.
Now install some sort of pull on the patch door so that you can reset it and pull it out.
This should work. Now if you want to go one step further, install some decorative hinges on the plug and allow it to swing open instead of taking it out.
You can decorate this up nicely to be functional and neat looking too.