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The variability and biases in the real-world performance benchmarking of deep learning models for medical imaging compromise their trustworthiness for real-world deployment. The common approach of holding out a single fixed test set fails to quantify the variance in the estimation of test performance metrics. This study introduces NACHOS (Nested and Automated Cross-validation and Hyperparameter Optimization using Supercomputing) to reduce and quantify the variance of test performance metrics of deep learning models. NACHOS integrates Nested Cross-Validation (NCV) and Automated Hyperparameter Optimization (AHPO) within a parallelized high-performance computing (HPC) framework. NACHOS was demonstrated on a chest X-ray repository and an Optical Coherence Tomography (OCT) dataset under multiple data partitioning schemes. Beyond performance estimation, DACHOS (Deployment with Automated Cross-validation and Hyperparameter Optimization using Supercomputing) is introduced to leverage AHPO and cross-validation to build the final model on the full dataset, improving expected deployment performance. The findings underscore the importance of NCV in quantifying and reducing estimation variance, AHPO in optimizing hyperparameters consistently across test folds, and HPC in ensuring computational feasibility. By integrating these methodologies, NACHOS and DACHOS provide a scalable, reproducible, and trustworthy framework for DL model evaluation and deployment in medical imaging.