Motion systems are a vital part of many industrial processes. However, meeting the increasingly stringent demands of these systems, especially concerning precision and throughput, requires novel control design methods that can go beyond the capabilities of traditional solutions. Traditional control methods often struggle with the complexity and position-dependent effects inherent in modern motion systems, leading to compromises in performance and a laborious task of controller design. This paper addresses these challenges by introducing a novel structured feedback control auto-tuning approach for multiple-input multiple-output (MIMO) motion systems. By leveraging frequency response function (FRF) estimates and the linear-parameter-varying (LPV) control framework, the proposed approach automates the controller design, while providing local stability and performance guarantees. Key innovations include norm-based magnitude optimization of the sensitivity functions, an automated stability check through a novel extended factorized Nyquist criterion, a modular structured MIMO LPV controller parameterization, and a controller discretization approach which preserves the continuous-time (CT) controller parameterization. The proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.