I would suggest the following:
Indiana Jones or Eric Draven (The Crow) [Allan Quatermain]
Conner McLeod (Highlander) [Dorian Gray]
Dr. Emmett "Doc" Brown (Back to the Future inventor) [Captain Nemo]
Blade (or Alucard from Hellsing) [Wilhelmina Harker / Murray]
Bruce Banner / Hulk [Dr Jekyll / Mr Hyde]
Dr. Sebastian Caine (Hollow Man) [Invisible Man]
Other (secondary) characters / contacts / etc
James Bond [Mr Campion Bond, the recruiter / leader in the comic]
and perhaps M?
Batman or Harry Dresdan [Sherlock Holmes]
Allan Quatermain is a big game hunter and explorer who can come back to life under certain circumstances. A sort of Lazarus Man, in a way. The Crow similarly can come back to life and has some skill in killing those hard to kill.
Another pointed out that Indiana Jones, having drunk from the Holy Grail, may have aged very very well - to the point of appearing a few decades younger than he should at the end of the twentieth century. (Well, actually they suggested he might be immortal, but I doubt that is the case.) So perhaps an Indiana Jones, appearing as aged as his father was in the third movie, could work for this role. A former / (current?) explorer / scholar could work well as a replacement of Allan Quatermain - especially as Indiana Jones was *based* off Allan Quatermain. While not as skilled in killing or as able to revive from the dead, in other respects Indiana works quite well. His (former) adventuresome life is behind him. He has aged well and skill has many of his skills (with the whip and gun), but he may be a little cynical due to having lived long enough to see most / all of his former friends die of old age. Note that Allan Quatermain regained his youth bathing in an African 'fountain of youth' (the springs of fire and life in the mythical african city of Kor, as I recall), so the connection with continued youth and water (drinking or bathing) works especially well with Indiana Jones.
Dorian Gray is an immortal who heals rapidly from even the worse injuries. He has a single weakness that can truly end his life - the destruction of his portrait. The Highlander (Conner McLeod) is similarly an immortal who can heal swiftly from even mortal injuries, but he has a single weakness that can truly end his life - beheading.
Captain Nemo is an explorer, an inventor, and a former terrorist with various eccentric personality traits (more so in the comic than in the movie). His greatest work is the novel form of travel - a submarine (in an age where such do not yet exist). Dr Emmett "Doc" Brown is similarly a somewhat eccentric inventor and explorer (of time) whose greatest work is a vehicle (either the De Lorean or the Train, although I would use the train for this type of group). He briefly worked with terrorists to gain the parts he needed - albeit he sabeutaged some of their works in the process as he himself was not a terrorist.
Wilhelmina Harker / Murray is a probably immortal semi-vampire, having some of their strengths and weaknesses but not all of either. It is hard to find a perfect match for her, but either Alucard (from Helsing) or Blade would work well, I think. Blade perhaps better than Alucard, who is strong enough to steal the show, so to speak. On the other hand, Alucard, working for Hellsing, has a british connection Blade lacks. Failing with these, one can always just use Wilhelmina again, although this is supposed to be a modern version as I recall.
Dr Jekyll is a genius scientist who turns into a super strong brutish being at times. Bruce Banner is also a genius scientist who turns into a super strong brutish being at times. I can't think of a finer comparison, actually.
The Invisible man is best replaced with the character from Hollow Man, as both he and Griffin (from the comic - who would have been in the movie had the studio not failed in their negotiations for the rights to use him) are deranged murders and rapists. I don't like the character, but he does work best for the role of Invisible Man. The hardest part is explaining how he regained a semblance of sanity (and borderline decency, for that matter).
In the comic, the League of Extraordinary Gentlemen is recruited and partially lead by Mr. Campion Bond - an ancestor of James Bond. Having his descendant work with the modern league not only sounds right, it also reaffirms the British tie to the organization. Retired M may or may not be a part of the organization, but I can just imagine how he, Banner, and Brown might get along. ^_^
Also in the comic, they are occasionally aided by Sherlock Holmes, so we should have a super sleuth amongst them as well. Perhaps Batman? Personally, I think Edogawa Conan would work best in this, or perhaps even a grown up version of Encyclopedia Brown. Worse comes to worse, we can use a more potent version than either of these (or even Batman) and go with Harry Dresdan. He certain is extraordinary and a moderately good sleuth besides.