Have you ever heard of Lincoln Ellsworth? He flew right across Antarctica in the 30s. No NASA military ice wall base. His plane had no "NASA conspiracy rigged GPS". And if the flat earth model was right, his plane would have run out of fuel LONG before he reached his destination. Ellsworth planned his flight based on a round earth, and succeeded.
In 1977, Pan American World Airways flew 120 paying passengers directly from South Africa to New Zealand, flying RIGHT OVER the south pole. And they did it MUCH quicker than it could have possibly happened if the Earth was flat. Plus, if the Earth was flat, the passengers would have seen Africa, Europe, Asia, and Australia out of the windows before reaching New Zealand. But no. They saw a small bit of Ocean, Antarctica, a little more Ocean, and New Zealand.
But who knows? You can always come up with excuses. Maybe there's a time warp near antarctica. Maybe there's a magic portal near the edge of the ice wall. Maybe they were abducted by gray aliens, who forced them to lie about what they saw. Or maybe, (god forbid) the Earth might actually be (gasp) round.
Today, you yourself can fly to the south pole for less than 50K dollars. You'll stay at the research station. And the pilots will happily fly you to locations that should be on the other side of the Earth if it was flat.
Of course, you might say, the South Pole station is not really in the South Pole, and it's all just a lie to fool brave explorers. And naturally you won't just accept the location your GPS says, as you believe it's rigged. Well, you're welcome to do it the old fashioned way and use a sextant just like Roald Amundsen did. But, of course, you'd sooner believe that the stars are a NASA hologram than that your flat earth model is wrong.