Ampan, I have not seen the flight plan and I dont know if the planned route took them over one, the other, or both of those towns.
Presumably they would have made use of ground based aids as long as possible before they had to rely entirely on the aircraft's on board systems, in which case the Invercargill NDB was likely their last check with the ground, though I may be quite wrong I dont think there was a VOR south of Christchurch in those days.
So what could the amendment to the position report mean? That they were 'lost' before they even left NZ? This is way out of my league I am afraid.