I think sooner is better. Interest has already been generated by opening discussion. It's summer so if we get teams together in the next two weeks people will have most of July and part of August to write before school starts. Can't really avoid work... and if we could all of us would have a different work thing to work around.

Schedule like this?
6.3.17 - 6.6.17 writer sign ups
6.7.17 - 6.9.17 Prompt selection
6.10.17 - 8.6.17 Writing
8.7.17 - 8.11.17 Posting (assuming there's 5 prompts)
8.12.17 - 8.27.17 Voting, people will also be voting during the posting week
8.31 Results announced

Adjust based on extensions.