They start buzzing when as you say they are on the way out or if the fuel lines have a restriction, have you changed the fuel filter? the problem has all the symptoms of this being blocked. If so then you may of got 2 dodgy pumps, try running the car and when it cuts out check the fuel pump if the area around the contacts is hot then this is a sign it's on the way out- an internal electrical/ mechanical problem will cause the terminals to get hot as the pump pulls more electrical load to compensate for high internal mechanical/ electrical resistance.

Steve