The ability to achieve controlled distributions of precipitates is one of the cornerstones of alloy optimization, in which small-angle scattering (SAS) serves as a powerful technique to characterize these distributions. One method of analyzing SAS data involves form factor intensity models, where modeled distribution parameters are obtained by solving a nonlinear least-squares (NLS) problem. However, the NLS method with a simultaneous search for all model parameters minimizes a very ill-conditioned objective function, which leads to a large number of search iterations and can give inadequate solutions. With the advancement of the 4th generation synchrotron rings and their potentially large datasets, it is increasingly important to find new and efficient numerical strategies for high throughput analysis. As a step in this direction, the purpose of this work is to investigate a pseudo-automatic numerical solution strategy based on the separable NLS method. The strategy is assessed in terms of correlation and precision of the model parameters, as well as convergence of the solution, using both synthetic and experimental scattering datasets. The decoupled fitting approach favors efficient parallelized batch fitting, which provides linear speedup for appropriate workloads. To support further development, the compounded features of the proposed solution strategy are packed into an easily accessible modular framework named python Small Angle Scattering Analysis (pySASA), which is openly available.