About this "briefed track":
Nobody seems to be addressing the fact that there were two, fundamentally different tracks in play.
One track was the track that ANZ wanted the crew, for optimum sightseeing, to follow. This track was the "sightseeing track". It was only around Antarctica and would be flown visually (with the AINS disengaged).
The other track was the one that would be programmed into the AINS. This track was the "AINS track" and was purely to get the aircraft from New Zealand to a position from where the sightseeing track could commence.
It would be folly to assume that these two tracks were intended to be one and the same. Mahon seems to have made that assumption and you, Desert Dingo, seem to be doing the same - or have I just misread your posts?
All the discussion I see in this thread about "the briefed track" fails to differentiate between the two.
Of course the passenger handout will show the sightseeing track. Of course the briefing will include detail as to where the sightseeing track should go.
The briefing should also have included some detail on the AINS track - given how fundamentally and conceptually different it was/is to the sightseeing track. Whether the briefing did or did not include this information seems to be in hot dispute.
I find it difficult to believe that the briefing would not have made references to the AINS track. The transition from the AINS track to the sightseeing phase - thence back to the AINS track was surely a significant aspect of how the flight would be conducted.
If I had been at the briefing and been told that the AINS track terminated at a point 27 miles west of McMurdo Station, I would have been asking "why does it terminate there? That makes no sense. It should terminate at the McMurdo Station TACAN".
Collins seems to have realised that the two tracks may have been different - hence his plotting the AINS track for himself the night before the flight.