I think you could do this with category permissions — have a category (or a subcategory) for each phase, with permissions like:
- Idea Gathering: anyone can post and reply
- Discussion: only moderators can post anyone can reply
- Voting: only moderators can post, and the post contains a poll. No replies.
- Building: posting limited by group to team members
And maybe you could use the kanban theme component in category mode with this — I haven’t tried anything like that, though.