We apply input allocation to a redundantly actuated platform driven by tilting aerodynamic propulsion units: the ROtor graSPing Omnidirectional (ROSPO). This platform represents a novel testbed for redundancy allocation designs in propeller-driven platforms. The control solution is based on a hierarchical architecture, made of a high-level controller for trajectory tracking, and a nonlinear input allocation algorithm. The algorithm exploits the input redundancy to take into account soft constraints associated with physical saturation limits of the actuators, and also induce reduced energy consumption. The actuator dynamics is fully taken into account in the framework and a rigorous proof of asymptotic tracking of time-varying references is guaranteed despite the impossibility of an instantaneous force execution. The experiments on the ROSPO platform clearly show the practicability and effectiveness of the proposed approach, as well as its scalability with different degrees of overactuation levels.