Props to theowest for pointing out a way to make stacking less painful. He commented:

"Using http://www.realtimesoft.com/ultramon/ I was able to get the pieces into a pile much faster. I simply centered the cursor using a hotkey: å in my case. http://i.stack.imgur.com/mKbVo.png"

As I understand, using this software you can assign a hotkey, which moves the cursor to the center of the screen. So picking up a piece and using the hotkey will make sure that all your pieces will be in a pile. Done right, one can pick up pieces using this method as well, which may minimize the amount of mistakes (skippable pieces).

Thank you for the tip!