The Generic Hypersonic Aerodynamics Model Example (GHAME) provides a practical benchmark for evaluating advanced control strategies for hypersonic vehicles. Its nonlinear dynamics and strong aero–propulsive coupling create challenges well suited to nonlinear inversion methods. This work develops a hierarchical control architecture based on time–scale separation, combining NDI for attitude and position control with Incremental Nonlinear Dynamic Inversion (INDI) for angular–rate and velocity control. The controller is implemented in MATLAB and Simulink and evaluated under synchronized and desynchronized sensor delays. The results show that delay synchronization markedly increases the admissible delay margin. The study also reveals a fundamental limitation in the lateral axis: the lateral-directional dynamics of GHAME are too fast to satisfy the time-scale separation assumption required by INDI, leading to unreliable linear stability predictions. In contrast, the longitudinal dynamics do satisfy this assumption and remain well suited to inversion-based control. Overall, the NDI–INDI structure is effective for the longitudinal motion when delays are synchronized, but the intrinsic speed of the lateral dynamics imposes a major constraint on its applicability for lateral control.