One of the "secrets" is that all the above-ground space is already within someone's jurisdiction ;)

No it isn't: http://bit.ly/wXJM9

Not sure it's legal to set up land-based economic activities without the blessing of at least one Antarctic-Treaty member countries. Even then, it's not legal to do mining or related activities.

I'm actually curious why you think this, have any more info? My presumption is that outside of legal jurisdiction anything is game. I guess existing land powers claiming whatever they want, such as the moon, may be legal but practically impossible to enforce.