Design an asynchronous task queue system in Python that can handle at least 10,000 concurrent operations. Your implementation should: 1) Use asyncio for event-driven concurrency, 2) Implement proper error handling and task recovery, 3) Include rate limiting and backpressure mechanisms, 4) Provide monitoring capabilities for task status and performance metrics, 5) Support task priorities and dependencies, 6) Include a mechanism for graceful shutdown. Explain your design decisions and provide a complete working implementation with test cases demonstrating its capabilities.