Why don't you prove that there is no edge by flying over antarctica and reach the other side. Put a camera on that plane and make a livefeed transmission on youtube.
It's been done (minus the live feed) multiple times. For example, team took a plane across both poles in November of 1965, including a nonstop leg from Buenos Aires to the south pole and on to Christchurch New Zealand, a flight which covered about 7000 miles and took them just over 14 hours. Going from Buenos Aires to Christchurch direct does not take you over the pole, they had to divert from the shorter great-circle route to cross the pole. This means they turned the aircraft between the two cities. Suppose there is no "south pole", suppose merely that they flew inland over the ice until they could no longer see the ocean, then made their turn for New Zealand. How many thousands and thousands of miles around the hypothetical edge of the earth would they have to go? That route from Buenos Aires to Christchurch is so much longer, in fact, that a Gleason Map route beginning heading north-west-ish over South America and curving across Central America, North America, the Pacific Ocean and Hawaii would be shorter than the substantially westward flight track followed by a great circle route. The point being, regardless of the details of their route, this plane did leave Bueno Aires, and did arrive in Christchurch some 14 hours later, with witnesses at both ends. On the Gleason Map, there is no way to plot a route that could be covered by that aircraft (Boeing 707) in that amount of time, nor indeed any route for which the 707 has enough fuel. The distances are simply too great.
And why should a live feed from this proposed experiment be any more compelling than the routinely scorned live feeds from the ISS? It would be trivial to fake a long-flight-over-ice video feed. Here's how I would do it: identical twin pilot #1 talks to the camera while boarding the plane in city #1, and during take off. At some pont he drops the camera, or a flight crew member gets too close to it, or turbulence shakes it, or some other distraction allows us to cut unnoticed to the camera on another plane, where identical twin pilot #2 finishes the flight and lands in city #2. We could even do a version of the
Penn & Teller bullet catch gag by having a dignitary in city #1 sign a souvenir and give it to 'the' pilot, to hand off to a dignitary in city #2 as proof of travel.