From a maneuverability perspective, the main advantage of tilting multirotor UAVs lies in the dynamic variability of the feasible executable wrench, which represents a key asset for physical interaction tasks. Accordingly, cant-angle selection should be optimized to ensure high performance while avoiding abrupt variations and preserving real-world feasibility. In this context, this work proposes a lightweight control framework for star-shaped interdependent cant-tilting hexarotor UAVs performing interaction tasks. The method uses an offline-computed look-up table of zero-moment force polytopes to identify feasible cant angles for a desired control force and select the optimal one by balancing efficiency and smoothness. The framework is integrated with a geometric full-pose controller and validated through Monte Carlo simulations in MATLAB/Simulink and compared against a baseline strategy. The results show a significant reduction in computation time, together with improved pose-tracking performance and competitive actuation efficiency. A final physics-based simulation of a complete wall inspection task in Simscape further confirms the feasibility of the proposed strategy in interacting scenarios.