No problem. Here is my idea: have 8 people (possibly the people in charge of Pokemon Dungeon or anyone that cares to sign up) that are Gym Leaders and 4 people act as the Elite Four (including a champion). Have these people make teams on Pokemon Online (or whatever online Pokemon battling system they care to use), and have a way for forum members to challenge the leaders and earn theoretical badges. After someone earned all 8 badges, they can challenge the Elite Four and proceed to challenge the Champion once the Elite Four are defeated (there could be a hall of fame for the victors). In essence, it would be like the way the games have been set up since day 1 except it includes members of the Pokemon Dungeon community as the trainers (and none of the "traveling the region battling an evil organization" stuff).
As for the teams, the Leaders and Elite Four could be restricted to having a single type of Pokemon (like the games), and the Champion could (and probably should) have a team of Pokemon of varying types. The people challenging the League could use whatever Pokemon they want, but there would of course have to be restrictions (such as no legendaries) so someone doesn't sweep the league with a team of 6 Arceus.
I have seen something like this a couple times before on forums and Facebook pages, but never with a forum with as many members as Pokemon/Zelda Dungeon. If the leaders (and other trainers, for that matter) are really into it, they can design a trainer card or gym badges for fun (I have even seen someone design a region for their League with made-up towns to go with the Gym Leaders). Just an idea.