A member of the Elite 4 faces the leader and the challenger and then decides who is the better gym leader.
Because like the leaders, the Elite Four sign up for the job. The only way this would work is if everyone agrees on who should be the Elite Four, then those people challenge all the candidates for gym leaders in the case where there are more than one candidate or if someone challenges that leader for leadership (wow, is that confusing or what?).
Basically, we pick the Elite Four as a group. Next, the Elite Four pick the gym leaders. If someone wants to take a leaders position, they contact the Elite Four, who will then decide if it's worth having a challenge. Finally, they will battle both the current leader and the would-be usurper., and will decide who's better for the job.
Is the gym league going to involve it's own special server, or are we just going to be usernames on shoddy's official server?