I've been talking with a few friends about a theme, so I wanted to submit this as well for people to have a gander at:
Legendary Pokemon could make for a great theme! A Pokemon Researcher (Propriety?) is interested in gathering information on Legendary Pokemon, and wants the challengers to help. We break the Legendary Pokemon down into three groups: The Elemental Legendaries, The Space-Time Legendaries, and the World Origin Legionaries. Each of the challengers has to go on a quest to discover some key information about the legendary pokemon (maybe a word scramble where each card has a letter on it, and they have to collect all the letters and make a word or something similar to get them interacting with other challengers), with the goal of using this information to try to capture one of the legendary pokemon (maybe we could have some Legendary pokemon Plushies from the Nintendo Store in New York as props for the Champion Photo Op/prizes if we can afford them, but probably not because they're pretty expensive.)
We could incorporate an Elite Six (two from each category; they don't have to be exact matches, just rough sorts of associations) and depending on what category you're in, you have to fight Four members: the two from your category and one from each of the other categories. The biggest reason for a larger E4- team is that East gets SLAMMED with people who want to play PPL. It would be to our advantage to offer up a larger Elite team.
If we want to incorporate the PAX Prime Plot, or the criminal organizations in some way, since the end goal is to capture one of the legendary, we could have the challengers find out that the champion is actually one of the crime bosses, who swoops in and captures the Legendary Pokemon before they can, and then the challenger has to battle them to get it back (Champion team could have that legendary on it).
It's nice because Legendary Pokemon are a big theme in the games, and everyone is familiar with them, but it doesn't require our gym leaders (or our Elite members, really) to have a specific theme.