My vote goes to Jimmy Forrest.
He was very famous in his day. As a student I spent some time researching the history of sport in Blackburn.
Reading through match reports from nineteenth century editions of the Blackburn Times it is very difficult to put forward a case for why he was such a great player. Journalists tended to write brief reports on the courage, tenacity, skill, cleverness of players but that doesn't really give us the detail we are looking for on Forrest when trying to put forward a case for his inclusion in the Greatest XI.
Plus the game, team formations, tactics were different back then. He was famous enough to have a popular football biography written about him entitled something like, Jimmy Forrest's Football Career with his Recollections and Opinions. (I read it and it wasn't any more literary than today's offerings). He was a working-class 'tape-sizer' in a cotton mill when he was discovered by Rovers and I believe he was the first professional to play for England. He was forced to wear a different style kit to distinguish him from his amateur team-mates.
Apart from his outstanding FA Cup achievements and the fact that he scored in some of those finals he went on to serve Blackburn Rovers as a director once his playing career finished. Is there a case to be made for Forrest influencing the club all the way up to the championship winning team of 1912?