Mechanically reconfigurable metasurfaces capable of translation, rotation, and permutation have attracted considerable attention for high-capacity optical information storage and full-color holographic displays, owing to their low-power and high functional scalability, despite the additional system-level complexity introduced by precision rotation stages. This study presents a differentiable inverse design framework for such metasurfaces, creating an accurate mapping between meta-atom geometries and their multi-channel optical responses across diverse optical dimensions. Using a deep neural network-driven, end-to-end optimization pipeline, the framework enables intelligent, iterative refinement of rotatable metasurface within constrained design space. Using this approach, we show high-fidelity holographic video display by rotating a single element in a cascaded metasurface doublet around the optical axis. The doublet enables pixel-resolved holographic imaging with 288 independent channels, and by switching input/output polarization states, the system demonstrates four distinct full-color dynamic holographic videos. This work establishes an alternative paradigm for optical parameter multiplexing and end-to-end inverse design in mechanically reconfigurable metasurfaces, suggesting applications in compact optical systems, dynamic holography, information processing, and optical computing.