Just from the video it almost seems like the pedal assembly itself is rubbing against something, as if it needs lubrication. Perhaps you press the pedal with force not only to the front, but to the side as well? Causing it to wear any plastic or rubber on the side to where it's metal on metal now? I'd take a look down there just to eliminate that possibility.
Does the sound sound like it's coming from the pedal itself?
Does the sound sound like it's coming from the pedal itself?