We present a novel predict-then-optimize framework for maritime search operations that integrates trajectory forecasting with UAV deployment optimization-an end-to-end approach not addressed in prior work. A large language model predicts the drifter's trajectory, and spatial uncertainty is modeled using Gaussian-based particle sampling. Unlike traditional static deployment methods, we dynamically adapt UAV detection radii based on distance and optimize their placement using meta-heuristic algorithms. Experiments on real-world data from the Korean coastline demonstrate that our method, particularly the repair mechanism designed for this problem, significantly outperforms the random search baselines. This work introduces a practical and robust integration of trajectory prediction and spatial optimization for intelligent maritime rescue.