Accurate prediction of coastal waves is critical not only for engineering design but also for safeguarding coastal communities through reliable navigation, flood defense, and shoreline management. Conventional parabolic equation models are computationally efficient but are limited in their reliability for wide-angle cases. We introduce a higher-order parabolic-equation model that augments a consistent nonlinear mild-slope framework with additional linear terms derived through a minimax approximation. The resulting formulation preserves triad wave–wave interactions while maintaining accuracy over a broad angular range. Three numerical models are compared: two nonlinear models and one linear counterpart. Laboratory data for wave transformation over an elliptical shoal provides a stringent validation case in intermediate water depth, a regime where traditional Stokes-type theories often prevail. Both nonlinear variants markedly outperform the linear baseline, capturing the observed growth and decay of wave amplitude and reproducing spatial patterns of free-surface elevation with high fidelity. The most developed model yields the highest accuracy, highlighting the importance of complete triad coupling for wide-angle, weakly nonlinear conditions. This enhanced model offers a practical and robust tool for engineering studies that require accurate prediction of wave refraction, diffraction, and shoaling over realistic coastal bathymetry.