At what stage should they have done this? Do you do this as you commence an instrument approach?
Around and around we go.
To answer your first question, after they had levelled at MSA
(FL 160) and a) couldn't verify by visually sighting the appropriate landmarks b) couldn't pick up the TACAN c) couldn't pick up the DME d) HF told them that the tower was trying to contact them on two different VHF frequencies but with no reply.
They could stay at MSA until they either get visual, pick up the TACAN and DME, or are in the sector that allows for safe descent to the south of Ross Island. If they had remained at MSA they would have picked up the TACAN /DME on passing Erebus, realised the error in planning, and that would be the end of the story. Now I'm not suggesting that they are an inferior crew for not doing that, but I am saying that that is a lesson we can take from this. MSA is there to keep you from hitting terrain. Can we at least agree that that lesson needed to be learnt?
If the passengers arrived in the descent sector area at FL160 and descended there it would not have been the end of the world.
As for the second question, I do verify my position prior to descending below MSA yes. I don't have to plot on a map but I would if the other four or five methods of doing it proved fruitless.
They were not in the wrong by descending when they did. Even Chippendale was of this view.
That does not answer the question. The question was "who issued the dispensation? "