Our work is split into work groups and projects. We run a kanban, deadline-based approach to match deadlines for conferences, journals, internal deadlines, publishing schedules, coordinating development work etc. The kanban is also useful for our continuing self-improvement process. The kanban is managed through our project-management tool, HacknPlan1.
We use HacknPlan for larger-scale project management. All members have to be a part of it. The Operations Team (Thomas) makes sure it is always up-to-date and that people report their tasks. We expect all to do it themselves but we get that everyone will have to get used to it.
Remember that we never work "for the Kanban". We work for Apart Research. If in doubt, always consider why a given task is needed. Question tasks and projects instead of blindly completing or forcing through tasks.