Current evaluation metrics for deep learning weather models create a "Statistical Similarity Trap", rewarding blurry predictions while missing rare, high-impact events. We provide quantitative evidence of this trap, showing sophisticated baselines achieve 97.9% correlation yet 0.00 CSI for dangerous convection detection. We introduce DART (Dual Architecture for Regression Tasks), a framework addressing the challenge of transforming coarse atmospheric forecasts into high-resolution satellite brightness temperature fields optimized for extreme convection detection (below 220 K). DART employs dual-decoder architecture with explicit background/extreme decomposition, physically motivated oversampling, and task-specific loss functions. We present four key findings: (1) empirical validation of the Statistical Similarity Trap across multiple sophisticated baselines; (2) the "IVT Paradox", removing Integrated Water Vapor Transport, widely regarded as essential for atmospheric river analysis, improves extreme convection detection by 270%; (3) architectural necessity demonstrated through operational flexibility (DART achieves CSI = 0.273 with bias = 2.52 vs. 6.72 for baselines at equivalent CSI), and (4) real-world validation with the August 2023 Chittagong flooding disaster as a case study. To our knowledge, this is the first work to systematically address this hybrid conversion-segmentation-downscaling task, with no direct prior benchmarks identified in existing literature. Our validation against diverse statistical and deep learning baselines sufficiently demonstrates DART's specialized design. The framework enables precise operational calibration through beta-tuning, trains in under 10 minutes on standard hardware, and integrates seamlessly with existing meteorological workflows, demonstrating a pathway toward trustworthy AI for extreme weather preparedness.