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In Projects view the status filter only distinguishes between flagged and unflagged. In context mode there are however 4 more, which include the due flags.

When I hit the 'Due' perspective (not sure whether it is available by default) I only see tasks with a due date.

Is that what you are trying to achieve? Only actions with a due date, or does it need to include any next actions for a project?

What about flagging the project (the flag on its actions is light, instead of bold). Does that help?