So, I avoided Final Crisis as much as possible -- is this Global Peace Agency (presumably that's the word, given the acronym) a plot element that came out of that, or is it something Ordway just came up with for his JSA run?
Yeah. It seems to be a kind of sort of replacement for Checkmate, for whatever reason Morrison thinks that is necessary. Theoretically, Final Crisis: Escape will explain more about it, but it's also doing the Prisoner thing.