This study explores the feasibility of stationary shoulder friction stir welding (SSFSW) for joining dissimilar extruded aluminum alloys, AA6082-T6 and AA6005A-T6, targeted for structural applications in the transportation industry. The key objective is to achieve higher welding speeds, up to 1.5 m/min, which is significantly higher than those typically reported for SSFSW in lap joint configurations. This increased welding speed is expected to reduce heat input, narrow the heat-affected zone (HAZ), and improve the microstructural uniformity and mechanical performance of the weld. Microstructural characterization via optical microscopy, scanning electron microscopy, and electron backscattered diffraction revealed extensive dynamic recrystallization within the stir zone, resulting in a refined average grain size of approximately 2.3 µm. Hardness mapping across the weld cross-section showed a significant reduction in hardness within the stir zone and HAZ, with the minimum hardness dropping to 65 HV from the base material hardness of 110–115 HV. High-speed SSFSW at 1.5 m/min produced sound joints with good lap interface bonding, despite the presence of a small root void. Lap shear tensile testing showed an average ultimate load of 3.8 kN, with all samples failing from the advancing side hook defect due to stress concentration. Fractographic analysis confirmed ductile failure modes with dimples in the fracture surface. These results suggest that high-speed SSFSW (1.5 m/min) is a promising technique for joining dissimilar aluminum alloys in lap joint configurations, offering potential advantages in microstructural refinement and mechanical performance compared to conventional methods.