The human metapneumovirus (HMPV) Fusion (F) glycoprotein is a high-priority target for "fusion-locking" agents that stabilize its metastable prefusion state. While monomeric catechins like EGCG are known antivirals, the molecular basis for the superior activity of structurally complex dimeric catechins remains poorly understood. We employed an advanced biophysical workflow, integrating 100 ns all-atom Molecular Dynamics (MD), Free Energy Landscape (FEL) analysis, and MM/GBSA thermodynamic integration to decode the Structure-Dynamics Relationship (SDR) of 210 Camellia sinensis (Green tea) phytochemicals. The results reveal a "Galloylation-Driven Anchoring" mechanism: the galloyl moiety of prodelphinidin A2 3′-gallate provides critical electrostatic complementarity to the Asp325-Asp336 acidic ridge. FEL analysis quantitatively demonstrates that this anchoring traps the F protein in a deep, kinetically stabilized global minimum (ΔG = 9.357 kJ/mol), effectively raising the energy barrier for the fusogenic conformational shift. This study provides a rigorous thermodynamic proof-of-concept for the use of dimeric natural scaffolds as precision fusion-locking agents, offering a roadmap for experimental biophysical validation.