Now I'm curious, how does this work with man-made islands? As in, can I build a really big raft/barge, tow it out to one of these areas that are unclaimed, anchor it down, and call it my own nation? Given of course that it'd be a hell of an engineering project, and getting resources out there would be a total pain, but is such a thing legally feasible? Or am I better of just buying a cruise ship that never docks?
Google "arcology". It's a portmanteau of architecture and ecology. It's not a new idea, but there hasn't yet been the right combination of technology, money, and motivation.
Also see wikipedia "principality of sealand". Some british nut tested a lot of the legal precedents. Short version, it totally works, although there was that one time his nation was conquered by mercenaries hired by a german lawyer, and his son was taken hostage. So, self defense is a very real concern.
It seems debatable whether a man made island is allowed to be a country. However you don't get your own territorial waters with an artificial island, which would make things very difficult.
Given that, there is no benefit to leaving exclusion zone. You can just set up in international waters much closer to shore.
Indeed, but most of it is very deep and won't be seeing any new islands soon.