I would recommend using Jon’s suggestion of a multi-wire circuit. Pulling one additional wire will change your 8.3 amp 120 volt circuit into a 4.2 amp 240 volt circuit. I haven’t done any calculations but would guess you could get away with #8 or even #10 conductors and be within your desired 3% voltage drop. Make sure you calculate each segment of the circuit not the full load at 1200’. This would take care of the lights but not the receptacle. You really need to know what is going to get connected to the receptacle to figure the drop. The customer might be willing to forget the receptacle if they realizes how much additional the larger wire will cost. If they definitely want the receptacle I would consider running a separate circuit just for it which will save splicing the larger conductors at each light.
Curt
