The local model fitting (LMF) method is a single-shot interferometric surface profiling algorithm that possesses nondestructive, fast, accurate, and robust measurement capabilities. To extend the measurement range of LMF, extensions based on multiwavelength light sources such as the multiwavelength-matched LMF (MM-LMF) method and the multiwavelength-integrated LMF (MI-LMF) method were proposed recently. MM-LMF is computationally efficient but it tends to suffer from phase unwrapping errors, whereas MI-LMF tends to be accurate but it is computationally expensive. In this paper, we improve the computational efficiency of MI-LMF by combining it with MM-LMF via local information sharing. Through actual experiments, we demonstrate that the proposed method is approximately 10 times faster than the original MI-LMF method, with measurement accuracy kept comparable.