Suggest modifying how the artificial collimation is rendered, either by making it truly invisible, or by not rendering the "box" for it when not aiming down the sight.
http://i.imgur.com/qBGBy6q.png
http://i.imgur.com/LEbyzcb.png
http://i.imgur.com/jxSz8X2.png
In the third link or the third attached image below (artificial collimation 2.png), the artificial collimation shadow stops just before the sight (circled), so I believe that it would be possible to just make them completely invisible.
EDIT: added to the attached files are two images with their color channels modified to highly exaggerate the shadow of the artificial collimation, and two false color images with just swapped color channels to partially exaggerate it while keeping the image quality and colors intact.