Shouldn't you actually mount the moon upside down for southern hemisphere mode? We all see the same moon, but some of us are not upside down relative to each other.
If the light didn't have the image of the moon on it, you could just reverse the phase sequence. But since it does, the moon image should also be upside down. Right?
(BTW, I had never thought of the moon being upside down in the other hemisphere before, but it's an interesting off-topic. I can't imagine how strange the moon must look upside down when traveling that far.)
[edit, forgot to mention: Awesome hack to make it work as it should have in the first place!]