Geological storage in salt caverns plays a critical role in managing energy resources, yet regional assessments often fall short in accounting for specific salt dome morphological variations that can significantly influence cavern engineering and storage capacity. To address this gap, we developed a refined approach to modeling salt domes, incorporating primary axis tilt, ellipticity, and conic taper. These geometric modifications are applied to a cylindrical baseline salt dome model to assess the effects on total salt volume, workable salt volume, and cavern storage potential. Case studies of four salt domes from the East Texas Salt Basin—Mount Sylvan, Boggy Creek, Steen, and Hainesville—validate the observed trends from the models. Our findings reveal that positive cone taper and primary axis tilt configurations enhance storage potential, leading to significant increases in potential cavern volume, while ellipticity and negative cone taper result in reduced storage capacities. The study underscores the importance of refining volumetric assessments by accounting for detailed morphologic variations, providing a more accurate framework for site-specific geological storage evaluations. Additionally, we discuss challenges related to intra-salt heterogeneities, including intra-salt deformation and mineralogical impurities, highlighting the need for improved site characterization to optimize the safety and efficiency of subsurface storage systems. This work contributes to the development of scalable and reliable geological storage infrastructure, essential for meeting future energy demands.