There could be another fourth factor to shape the shadow the moon casts on the Earth surface: atmosphere refraction. Atmosphere isn’t a static, rigid and perfectly uniform and transparent shell of gas. It’s exactly the opposite. Atmosphere winds, humidity, composition, pressure and temperature can change wildly, so does its refraction capabilities. In my opinion the shape of the shadow cast by the moon will also be subject to these factors, to a certain extent.
Could this be the case?