Implementation of Model Predictive Control (MPC) on hardware with limited computational resources remains a challenge. Especially for long-distance maneuvers that require small sampling times, the necessary horizon lengths prevent its application on onboard computers. In this letter, we propose a computationally efficient tube-based shrinking horizon MPC that is scalable to long prediction horizons. Using move blocking, we ensure that a given number of decision inputs is efficiently used throughout the maneuver. Next, a method to substantially reduce the number of constraints is introduced. The approach is demonstrated with a helicopter landing on an inclined platform using a prediction horizon of 300 steps. The constraint reduction decreases the computation time by an order of magnitude with a slight increase in trajectory cost.