Do Australians say "down north"?
Solution 1:
The maps you see with south at the top are generally considered novelties, and are not seriously considered. The worldwide convention for maps is to orient north at the top.
I have never heard the expression "down north" when referring to the northern hemisphere. A Google Ngram search shows that sometimes people say "down north" when living in an area where the rivers generally run northward toward the sea (such as arctic Canada).