I think this might be helpful. It shows up next to the ship details window if you click on a weapon modules icon (or on the actual physical turret in the main view). This shows the range overlay, but now it also shows shots fired, hit/missed and the damage done, although it’s overall, not a specific target.
Tell me your thoughts. Is this too simplistic or abstract? I can see this being useful for spotting turrets that fire constantly and hit nothing. Click to enlarge it.