Elect a manager
You need someone to be the Mayor of GroupWorkVille. It really helps to have someone responsible for keeping everything organized and moving forward. As you know, in a ten-week term, a little slacking now can create an impossible emergency later!
This sounds like a totally thankless job, right? Your group can negotiate the work involved in the entire project to make being the project manger more enticing, for example, your group's PM may get a smaller writing section or an easier section of the project.