Since the perspective doesn't change, you could use any software that allows you to paste in multiple screenshots.
1. Take screenshots that cover the area you wish (i.e. go to the top left, take a screenshot, move right, take another - make sure there's a little overlap)
2. Import them all using the tool of your choice. You will be able to match them up, pixel for pixel...
3. When done, zoom out and crop the edges so it's nice and rectangular (or square)
It's a little work, but unlike with photographs, where things aren't pixel-perfect, this is.