Building a Web App using Drupal
Creating your own install profile doesn't need to be a big project in itself, especially for Drupal 7, that has simplified making install profiles. Features also helps a lot, making it easy to save settings, content types, views etc in a module.

All you really need to do in the install profile is to


Enable modules
Save settings
Enable blocks (maybe)
Create content (maybe)


I suggest that you build your own install profile that fits your needs, instead of trying to find one. You could start out with how it's done in Open Atrium, and just edit it to fit your needs.