Ok, so just a quick rundown of the requirements:
-game has to be educational, with a focus on developing leadership skills.
-at the end of each week there is a challenge relating to a particular theme. During that week players are expected to prepare for the challenge
-the players work on their own, but come together in groups to compete in the challenge.
-the players communicate via email and a website, physical contact should not be necessary
The reason why I asked about the ARG is because a key element of an ARG is that players receive clues they have to piece together in order to advance in the game.
I'm thinking along the lines of each player receives a series of tasks that get rewarded with different parts that need to be assembled for the challenge. With the exception of one task, each task is shared by one or more members on their team. If the members fail to communicate, they will end up having wasted valuable time with parts they don't need.
Say for example the challenge was to build a race car that would race against other groups. Each task would lead to a different piece of the car (a wheel, engine part, etc). Person 1 might have tasks that lead to a steering wheel, wheel and a headlight. Person 2 might have tasks that lead to a steering wheel, a break and an engine. If they don't coordinate properly with each and teammates,they will end up with a car with two steering wheels and no engine.
-the tasks themselves could take the form of puzzles or quizzes they email to the game master (either you or an automated checking system) who then emails a code for a part. At the challenges they then email the codes back to the game master for their parts. Parts could be assembled in a GUI applet manually as part of the challenge or the game master could give them the assembled piece and the challenge is just how they control what they're given.
hope this helps somewhat.