Do cheap servos have potentiometers that originally sweep some 300 degrees and they use only 180 degrees? If that's true, then it could be hackable. The optimal thing would of course be a servo which turns 180 degrees if it's supposed to turn 180 degrees, but the internal movement of the potentiometer sweeper would be 300 degrees, if that's what the potentiometer can perform. It would be achieved through the gears.