Autonomous landing of Uncrewed Aerial Vehicles (UAVs) on oscillating marine platforms is severely constrained by wave-induced multi-frequency oscillations, wind disturbances, and prediction phase lags in motion prediction. Existing methods either treat platform motion as a general random process or lack explicit modeling of wave spectral characteristics, leading to suboptimal performance under dynamic sea conditions. To address these limitations, we propose SpecFuse: a novel spectral-temporal fusion predictive control framework that integrates frequency-domain wave decomposition with time-domain recursive state estimation for high-precision 6-DoF motion forecasting of Uncrewed Surface Vehicles (USVs). The framework explicitly models dominant wave harmonics to mitigate phase lags, refining predictions in real time via IMU data without relying on complex calibration. Additionally, we design a hierarchical control architecture featuring a sampling-based HPO-RRT* algorithm for dynamic trajectory planning under non-convex constraints and a learning-augmented predictive controller that fuses data-driven disturbance compensation with optimization-based execution. Extensive validations (2,000 simulations + 8 lake experiments) show our approach achieves a 3.2 cm prediction error, 4.46 cm landing deviation, 98.7% / 87.5% success rates (simulation / real-world), and 82 ms latency on embedded hardware, outperforming state-of-the-art methods by 44%-48% in accuracy. Its robustness to wave-wind coupling disturbances supports critical maritime missions such as search and rescue and environmental monitoring. All code, experimental configurations, and datasets will be released as open-source to facilitate reproducibility.