No matter which way you look at it, cutting the neutral line will not turn the lights off. You have already noted there is voltage between the phases and that is what makes them light up. The three phases are not carrying the same voltage, they carry the same waveform but phase shifted 120 degrees between them.
Surely the street lights have their own wiring, you need to isolate all three phases with a contactor but only on the wiring to the street lights. You can leave the neutral permanently connected if you wish although for safety reasons it would be wise to isolate it as well.
Brian.