These examples don't refute the flat earth theory. First of all the New Zealand/Australia trips don't even go to the south pole. And the South Africa trip does not mention the route they take to the south pole. For all we know they may come in a little past the 80 degree south line from the African point, but then skirt around westerly to the South American point, and then go the the south pole from there. In order the refute the flat earth theory you would have to know that the trip approaches the south pole directly going only south from the African entry point. But how would we know that?
Not quite right, you only need to prove the existence of the South Pole to refute the flat earth argument completely, unless you can come up with a flat earth model that has two poles.
How can you tell if you are actually at the geographic South Pole? Well, first you could look up and notice that the stars are revolving around a point that is directly overhead, but that might not work too well in mid summer, stars would be hard to see, since the sun never sets, ( another proof of the globe ), you could watch the sun moving around the horizon from right to left. That would prove you were at the South Pole, and not teleported magically to the North Pole. Where the sun would be going the opposite way around the horizon.
The flight cost is 62,000 euro for a 9 day expedition, and you would then be able to report back here, confirm or deny the truth of what I'm saying.