Shear wave elastography relies on accurate motion tracking for stiffness estimation. However, noise and rigid medium structures degrade shear wave quality, particularly when distant from the push location. We propose ShearMoFit, a dual-plane motion cleaning technique to improve robustness to noise and amplitude loss. Each time-lateral (t-x) plane was biaxially normalized and summed, followed by flood-fill to isolate the shear wave path. RANSAC polynomial fitting of peak positions in axial-lateral (z-x) planes was used to create spatially decaying masks that enhance wavefront localization and noise suppression. Applied to noisy Loupas-tracked, directionally filtered shear wave data acquired from experimental breast phantom, ShearMoFit facilitates higher SNR and cleaner shear wave reconstructions. The method also restores attenuated shear waves, expanding the usable field of view. ShearMoFit offers improved shear wave quality for accurate stiffness estimation, aiding diagnostics, treatment monitoring, and clinical translation for elastography.