Hmm, the Earth is in the wrong position for the end of August so 10th September is still a winner. I think that the Moon's position might not be accurately drawn unless we're looking at a different year altogether.
OK, I had the moon going round the wrong way! This means is has done around 3 1/4 orbits, given that 6th September would be 3 orbits, it brings us back to the 13th of September (or thereabouts).
Also, we're talking about three days difference to get to back to the 10th, which is more than 10% of the moon's orbit, or around 38 degrees, which I'm sure would be noticeable on the position of the moon. I think we're much more likely to be talking about the 13th (give or take a day) than the 10th.