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For industrial applications of self-assembled wormlike micelles, measurement and characterization of a micellar material's microstructure and rheology are paramount for the development and deployment of new high-performing and cost-effective formulations. Within this workflow, there are significant bottlenecks associated with experimental delays and a lack of transferability of results from one chemistry to another. In this work, we outline a process to predict microscopic and thermodynamic characteristics of wormlike micelles directly from rheological data by combining a more robust and efficient fitting algorithm with a recently published constitutive model called the Toy Shuffling model [J. D. Peterson and M. E. Cates, J. Rheol. 64, 1465–1496 (2020) and J. D. Peterson and M. E. Cates, J. Rheol. 65, 633–662 (2021)]. To support this work, linear rheology measurements were taken for 143 samples comprising a common base formulation of commercial sodium lauryl ether sulfate, cocamidopropyl betaine, and salt (NaCl). The steady state zero shear viscosity evident in linear rheology was measured in duplicate via direct steady and oscillatory shear experiments. Fitting the collected data to the model, we found trends in the microstructural and thermodynamic characteristics that agree with molecular dynamics simulations. These trends validate our new perspective on the parameters that inform the study of the relationship between chemical formulation and rheology. This work, when implemented at scale, can potentially be used to inform and test strategies for predicting self-assembled micellar structures based on chemical formulation. [ABSTRACT FROM AUTHOR]