Solving large non-negatively constrained least squares systems is frequently used in the physical sciences to estimate model parameters which best fit experimental data. Analytical Ultracentrifugation (AUC) is an important hydrodynamic experimental technique used in biophysics to characterize macromolecules and to determine parameters such as molecular weight and shape. We previously developed a parallel divide and conquer method to facilitate solving the large systems obtained from AUC experiments. New AUC instruments equipped with multi-wavelength (MWL) detectors have recently increased the data sizes by three orders of magnitude. Analyzing the MWL data requires significant compute resources. To better utilize these resources, we introduce a procedure allowing the researcher to optimize the divide and conquer scheme along a continuum from minimum wall time to minimum compute service units. We achieve our results by implementing a preprocessing stage performed on a local workstation before job submission.