I gave it another go, but I couldn't see how vertically swinging the shot can be more accurate than constantly stabilizing the gun and swinging right/left. Vertical and horizontal swings don't differ. It's just that there's more horizontal space for the bullet curves than vertical due to the ceiling. Is the vertical weapon axis wobble intended as an additional element of difficulty, or is it part of your intended input mechanic? For me the gun's vertical axis goes crazy after a couple of relatively subtle movements and becomes virtually uncontrollable unless I stabilize it with RMB first. Am I not supposed to do that?
The problem with the 'relatively slow process' of swinging in the third level is, that I don't have the time to execute it. I get shot first.
Maybe adding a few intermediate levels with a more gradual increase of difficulty would help. One or two scenarios with stationary targets before moving on to moving targets could do it. You know, with different geometrical challenges, so the player has time to develop a feel for what's going on. I can imagine that many players would hit the first target more by chance than by skill.
One peculiar thing happened to me while playing level 3 again: I happened to press RMB the moment the turret's beam hit me and somehow I managed to 'catch' the beam. Is that a remnant of a mechanic you were experimenting with?