Sorry if my schematic or description was unclear. The switches are for UI menu navigation, so they're related to the display in that sense, but none have any direct relationship to the enable pin in question.I had trouble reading the schematic, but assumed it was the micro that enabled the LCD based on some signal it got from the switches. Maybe that's not the case. I would think the grounds within the case would be close to the same (short leads), but maybe not. Might need to drag out the scope.
Also, I may be using a misleading name for that pin. I believe there are two enable pins: backlight enable and write enable. The latter determines when a command or character to display (defined by the states of the data pins) is acted upon (executing the command or displaying the new character.) So the process as I understand it is set all the data pins to the values you want, then toggle write enable pin on/off (or off/on, can't remember) to enact the change, then set data pins to new values and repeat.
Although that enable signal definitely normally comes from the micro, my suspicion is that either the enable pin/trace within the display housing is cycling high/low in response to noise, or more likely that the ground reference within the housing is moving such that the enable pin appears to the display to be moving because of the changing ground reference. Does this make any sense or am I just talking crazy?!
So to put it another way, I *think* that everything is perfectly fine on the micro side, and that the effect of the noise is just within the display housing.