Robots are increasingly being deployed in agriculture to support sustainable practices and improve productivity. They offer strong potential to enable precise, efficient, and environmentally friendly operations. However, most existing path-following controllers focus solely on the robot's center of motion and neglect the spatial footprint and dynamics of attached implements. In practice, implements such as mechanical weeders or spring-tine cultivators are often large, rigidly mounted, and directly interacting with crops and soil; ignoring their position can degrade tracking performance and increase the risk of crop damage. To address this limitation, we propose a closed-form predictive control strategy extending the approach introduced in [1]. The method is developed specifically for Ackermann-type agricultural vehicles and explicitly models the implement as a rigid offset point, while accounting for lateral slip and lever-arm effects. The approach is benchmarked against state-of-the-art baseline controllers, including a reactive geometric method, a reactive backstepping method, and a model-based predictive scheme. Real-world agricultural experiments with two different implements show that the proposed method reduces the median tracking error by 24% to 56%, and decreases peak errors during curvature transitions by up to 70%. These improvements translate into enhanced operational safety, particularly in scenarios where the implement operates in close proximity to crop rows.