Hand-intensive manufacturing processes, such as composite layup and textile draping, require significant human dexterity to accommodate task complexity. These strenuous hand motions often lead to musculoskeletal disorders and rehabilitation surgeries. Here we develop a data-driven ergonomic risk assessment system focused on hand and finger activity to better identify and address these risks in manufacturing. This system integrates a multi-modal sensor testbed that captures operator upper body pose, hand pose, and applied force data during hand-intensive composite layup tasks. We introduce the Biometric Assessment of Complete Hand (BACH) ergonomic score, which measures hand and finger risks with greater granularity than existing risk scores for upper body posture (Rapid Upper Limb Assessment, or RULA) and hand activity level (HAL). Additionally, we train machine learning models that effectively predict RULA and HAL metrics for new participants, using data collected at the University of Washington in 2023. Our assessment system, therefore, provides ergonomic interpretability of manufacturing processes, enabling targeted workplace optimizations and posture corrections to improve safety.