Why are true headings followed above 73N in the northern hemisphere, whereas in the southern hemisphere the change is made at 60S?
Earth's magnetic field is not symmetric north to south.  In particular,  the magnetic declination can get significantly larger at a given southern latitude than it does at the corresponding northern latitude.  This can be seen by looking at a world declination map:

Curves of a given declination reach much lower southern latitudes than they do northern latitudes.  For example, the highlighted curve is 40° west of north declination;  its southernmost point in the northern hemisphere is at about 75°N, but its northernmost point in the southern hemisphere is at 35°S (!).  Another way this manifests is that the South Magnetic Pole is at a significantly lower latitude than the North Magnetic Pole (~65°S vs. ~85°N).
As to why the Earth's magnetic field is so asymmetric, that's a question for Earth Science.SE.  My understanding is that you may not get a good answer over there either;  the behavior of Earth's magnetic field is complex and not fully understood.