Now this is an awesome question in my opinion. Some musings on this:
How much gonzo is enough? Should the adversaries of the league only be inspired by existing villains and their aftereffects or can outside canon be introduced? Must the whole thing adhere to the model the movie and the comics presented, may the players extrapolate their own deviations from the established characters cannon? What should the tone be like, serious in its presentation like in the comics, with some ugly realism/fridge horror thrown into the mix?
On another note, the french jeu de role ''Brigade Chimerique'' is very similar to the League of Extraordinary Gentlemen, concentrating on the ''superheroes of europe'' and their existance between the world wars. The ''forgotten history'' angle is what drew me into that game.