Personally I think your best bet is to use a funnel-like process.
Team generates ideas. No criticism at this point just write stuff down. Wikis, Skype, group chat are all good tools here. Each person should generate ~20 ideas at this stage.
Filter through ideas. You can do this alone or with the team. Most likely start by picking a few key qualities to optimize for. (e.g. novelty, depth, time to create.) Put ideas into buckets, start eliminating ones that don't meet the cut. You should end up with ~1 idea per a person at this stage. Consider using Excel or Google Spreadsheet to help you slice & dice and visualize your data.
Prototype ideas, still no coding or very limited coding. Best bet would be to use pen & paper to draw out some of the interactions. You could also use something like XNA, Game Maker, or Flash to prototype ideas quickly and cheaply. Identify the best one at this point.
Implement more features in waves, no more than 1 day per a feature. At the end of each day test what you have and measure it against the qualities you were optimizing for in step 2. Cut the features that don't seem to be helping and do more of the stuff which is. Most likely use version control to distribute source code for prototypes, e-mail, a wiki, etc for feedback.
Tools to use:
- Git, SVN for version control
- DropBox, Git, SVN for distributing builds
- E-mail, Wiki, Google Docs, Google Wave, Chatterous, Skype for feedback, discussion
- GitHub, Mantis, Jira for issue tracking
- SCRUM, Kanban for development process
- Excel, Google Spreadsheets to work with feedback / break features down and visualize results
Edited to add mention to spreadsheets, we often forget it but Excel is easy to use, powerful, and creates visuals which communicate a lot quickly