This paper presents a comprehensive study on optimizing a water-cooled automotive traction Wound Field Synchronous Machine using an inverse-cosine pole-shaping variant with pole-shoe extensions. The objective was to maximize torque and minimize total loss at base speed, considering constraints like torque ripple, thermal loading, and mechanical stress yield factor. The optimization of the baseline design was conducted via a differential evolution algorithm. The design effectively fulfills all design requirements, maintaining the active volume constraints. Through iterative post-optimization adjustments of the pole shape, the effects on machine performance were analyzed. The inverse-cosine pole-shaping with novel pole-shoe extensions proves to be a superior approach. Compared to a design without pole-shoe extensions (6.49% torque ripple), the baseline design enables a ripple reduction of 2.45 %. The conclusion is that the pole-shoe extensions have considerable influence on torque-ripple.