You're forgetting a thing. We've calculated/observed this phenomenon from several hundred thousand kilometres away. To put it in perspective: the Moon, in average, is about 30 arcminutes in the sky (one arcminute is 1/60th of a degree - so 30 arcminutes is half a degree). As you stated, the diameter of the moon is about 3475 km. That gives us, at that distance (3475/30) ~116km per arcminute. Which in turns is almost 2km per arcsecond. 2km is 2,000,000 mm. Which means that 1mm is 1/2000000th of an arcsecond. With 3.5mm, that's about 0.000000175 (if my math is right) arcsecond. We've got equipment to observe and calculate something close to one billionth of a degree to a degree of certainty that makes it significant instead of a rounding error.