First-principles modeling, experimental, and thermodynamic methodologies were integrated to facilitate a fundamentally guided investigation of quaternary complex hydride compounds within the bialkali Na-Li-Al-H hydrogen storage system. The integrated approach has broad utility for the discovery, understanding, and optimization of solid-state chemical systems. Density functional theory ground-state minimizations, low-temperature powder neutron diffraction, and low-temperature synchrotron X-ray diffraction were coupled to refine the crystallographic structures for various low-temperature distorted Na2LiAlH6 allotropes. Direct method lattice dynamics were used to identify a stable Na2LiAlH6 allotrope for thermodynamic property predictions. The results were interpreted to propose transformation pathways between this allotrope and the less stable cubic allotrope observed at room temperature. The calculated bialkali dissociation pressure relationships were compared with those determined from pressure-composition-isotherm experiments to validate the predicted thermodynamic properties. These predictions enabled computational thermodynamic modeling of Na2LiAlH6 and competing lower order phases within the Na-Li-Al-H system over a wide of temperature and pressure conditions. The predictions were substantiated by experimental observations of varying Na2LiAlH6 dehydrogenation behavior with temperature. The modeling was used to identify the most favorable reaction pathways and equilibrium products for H discharge/recharge in the Na-Li-Al-H system, and to design conditions that maximize the theoretical hydrogen reversibility within the Na-Li-Al-H system.