This paper presents a novel method for the design of gain-scheduled output feedback controllers in the presence of hidden coupling terms, which naturally arise when endogenous signals are used as scheduling parameters. In this case, the controller gains vary with respect to system variables, leading to inner loops between the system and the linearized gain-scheduled controller dynamics. Such effects, also known as parasitic feedbacks, are inherently difficult to handle in classic gain-scheduling control design and are often omitted, which might result in performance degradations or even destabilization of the closed-loop system. This paper shows how such a pitfall can be avoided through the application of self-scheduling and eigenstructure assignment techniques. In this context, the main contribution of the present work is the extension of eigenstructure assignment-based self-scheduling techniques for explicit hidden coupling terms handling. The viability of the proposed method is illustrated through a pitch-axis missile autopilot benchmark problem.