Ok, I will share a few thoughts on this...
As I see it: According to Flat Earth Theory..Antarctica is a mysterious out of bounds region. It represents some kind of edge or barrier to the known world.
This region has been lied about by worldly powers in a massive deception. The worldly powers have banned travel there, banned fly overs etc and it is in any case a difficult environment to reach and survive in.
Those who aim to deceive the public often employ "controlled opposition" groups and shills to derail both productive debates AND useful actions that would destroy the deception.
So (whether difficult or not) the obvious course of action in resolving the question of Antarctica is to explore the region, to observe it and make records thereof to share with key people in the population as a prelude to mass awakening regarding the truth of the matter.
In such a case we have: human exploration, telescopes etc as suggested by Mostlyharmless and remote exploration via technology eg a remote controlled flier or balloon.
None of these options should be discounted. In fact each suggestion should be worked on and planned. Difficult goals should be broken up into smaller more achievable goals and worked on bit by bit.
So, talking of controlled opposition, would they be encouraging explorations like this or discouraging them?
I am not implying that everyone dismissing the project on this Forum are controlled opposition. However in contemplating scenarios discussed above (eg a massive hundreds of years old deception) it seems there is likely to be a lot of 'conditioning' in people discouraging them from actually making attempts to explore the edges. That conditioning may take the form of discouraging beliefs about the impossibility or great difficulty of such exploration projects. Therefore those who find themselves initially discouraging such exploration should look closely at the hidden inner causes of such a position and then adjust their position as appropriate.
Apart from the hypothetical controlled opposition and apart from disempowering conditioning there may also be an ego based fear-a fear of actually being proved wrong after all. We should not be attached to our beliefs no matter how long we have held them, or how much effort we have put into promoting them. We should be loyal to truth.
The surest way to failure is to not even try. So lets look again at Pongo's useful post above:
http://forum.tfes.org/index.php?topic=2676.msg66877#msg66877which outlines some of the steps needed and build from there.