Reconstructing strand-level 3D hair from a single-view image is highly challenging, especially when preserving consistent and realistic attributes in unseen regions. Existing methods rely on limited frontal-view cues and small-scale/style-restricted synthetic data, often failing to produce satisfactory results in invisible regions. In this work, we propose a novel framework that leverages the strong 3D priors of video generation models to transform single-view hair reconstruction into a calibrated multi-view reconstruction task. To balance reconstruction quality and efficiency for the reformulated multi-view task, we further introduce a neural orientation extractor trained on sparse real-image annotations for better full-view orientation estimation. In addition, we design a two-stage strand-growing algorithm based on a hybrid implicit field to synthesize the 3D strand curves with fine-grained details at a relatively fast speed. Extensive experiments demonstrate that our method achieves state-of-the-art performance on single-view 3D hair strand reconstruction on a diverse range of hair portraits in both visible and invisible regions.