Flapping-wing vehicles regulate aerodynamic forces and moments through coordinated variations in stroke, deviation, and pitch motion. Because the resulting loads depend on both the instantaneous wing configuration and its preceding motion history, recovering suitable wing kinematics from a desired aerodynamic trajectory is a challenging inverse problem. Existing sequence models capture temporal dependencies, while spectral methods can exploit the periodic structure of flapping motion. However, unrestricted frequency-domain augmentation may interfere with temporal representations and produce inconsistent corrections across kinematic variables and prediction horizons. We propose the Bounded Channel-Adaptive Spectral Residual Gated Recurrent Unit (BCS-GRU), which retains recurrent temporal prediction as its primary representation and restricts spectral information to a controlled output-specific correction. We further introduce a causally aligned forward-consistency objective that evaluates predicted kinematics through a separately trained and frozen aerodynamic surrogate. Experiments under a unified episode-level protocol show that BCS-GRU improves inverse prediction over recurrent and adaptive-spectral baselines, with greater benefits at longer prediction horizons. Forward-consistent fine-tuning further improves surrogate-based aerodynamic consistency while maintaining mean kinematic accuracy. These results demonstrate that controlled spectral correction and forward-consistent learning provide an effective framework for history-aware inverse modelling of flapping-wing aerodynamics.

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