The flights over Antarctica have always been "interesting" for we operators of said services. On the B744 we had as diversion ports Christchurch or Punta Arenas. It got out to 3h55 diversion time. The near impossibility of a good outcome at Punta Arenas is for another thread. As has been pointed out, number of engines is irrelevant.
Now think about a cabin fire. It is well known that with a real fire you will be on the ground in about 15 minutes - in pieces or after a forced landing. The advice for flights over the deep south is to fly north until you have to ditch. Simply put, you lose the airframe and all POB coz the best ditching in the world just means that you die shortly after. The Southern Ocean sea temps are around 12*C so you quickly die of exposure. Great food for thought for us operators. A failing gasper fan actually caused smoke in the cockpit on one of those trips about 75*S. Luckily it stopped smoking after the checklist procedures, roughly 8 minutes. Severe damage to the undies of the 4 pilots!!!
I always enjoyed the technical challenge of the operation SYD-EZE-SYD but wasn't too keen to stay in Buenos Aires. Terrible place for a crew slip.