One of the challenges in computational acoustics is the identification of models that can simulate and predict the physical behavior of a system generating an acoustic signal. Whenever such models are used for commercial applications an additional constraint is the time-to-market, making automation of the sound design process desirable. In previous works, a computational sound design approach has been proposed for the parameter estimation problem involving timbre matching by deep learning, which was applied to the synthesis of pipe organ tones. In this work we refine previous results by introducing the former approach in a multi-stage algorithm that also adds heuristics and a stochastic optimization method operating on objective cost functions based on psychoacoustics. The optimization method shows to be able to refine the first estimate given by the deep learning approach and substantially improve the objective metrics, with the additional benefit of reducing the sound design process time. Subjective listening tests are also conducted to gather additional insights on the results.