I had always thought this society was just a fictional joke, but after reading some of your arguments i have come to realize that you actually might be serious. I would rather not waste my time reading your evidence, because there are so many flaws with this "theory" it's overwhelming.
First of all, to settle this once and for all, why doesn't one of the most loyal members of this society, attempt to attend the schooling to actually join NASA? If you were able to join and saw for yourself that the earth is not flat, would that not prove your theory wrong? As serious as you take this, i would think someone would have tried this by now....
Also, an even more simple solution, are you telling me nobody in this society owns a boat? You can't try to sail around the world yourself? I realize you must have some sort of circular flat layout to your map that would make traveling between countries possible, but what if you tried to sail on a route that would not be possible according to your map? If you could actually sail it, then your map would have to be wrong wouldn't it? Are you really trying to convince me that people that own their own private ships and sail around the world are somehow all apart of this conspiracy as well? The second they reach the end of this flat earth, NASA is waiting for them, brainwashes them into thinking the earth is round and to forget what they saw?