What do you think about this for a solution? If the camera is panning, with Abe being (presumably) fixed in the centre of the screen, then think about where that slig would have to be- right at the edge of the viewable area, to the point where it is close to going off screen.
With the flick screen system, if we walked into a new screen to see a slig shouting 'FREEZE!', we had to turn and run straight away or be shot. Also think how, if you stopped running whilst being chased, the slig had to stop to shoot- they couldn't run and gun. In fact, if you were quick, you could stop briefly then carry on running, and the slig would do the same
Point is, the slig needs to stop to shoot you. He will only stop if you do, in which case you'd be shot anyway just like in the classic games. But if he tries to shoot while you are running, he will disappear off screen- and just like AO/AE, you can't be shot from off screen!
Just a thought- it doesn't seem too different to the original's mechanics actually!