真剣にやって 'do it seriously' — a te-form request. 学園祭 'school festival' — a major annual event in Japanese schools. 待ってくれない 'won't wait for us' personifies the deadline. 大詰め 'final stage, climax' comes from kabuki theater. なんだから at the end gives an insistent, explanatory reason: 'because we're already...'