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While 3D Gaussian Splatting (3DGS) provides an efficient and explicit representation for novel view synthesis, enforcing stylistic coherence across viewpoints remains challenging. Existing 3D stylization methods typically apply 2D feature-matching losses independently per rendered view, which leads to unstable style allocation, many-to-one feature reuse, and limited cross-view consistency. We propose a capacity-controlled framework for multi-view stylization of 3DGS, grounded in optimal transport. Specifically, we reformulate local style matching as a semi-balanced optimal transport problem. By introducing explicit column-capacity constraints with tunable strength, our formulation mitigates many-to-one matching and enables controllable allocation of style features. This transport-based objective provides a principled mechanism for balancing feature coverage and stylistic diversity while maintaining stable correspondences across viewpoints. To further enhance cross-view coherence, we incorporate a novel cross-view matching guidance to constrain correspondences between scene content and style patterns. In addition, we introduce several geometric regularizations to enhance the vanilla 3DGS, thereby enabling optimized Gaussian primitives to represent finer-grained textures during stylization. Extensive experiments demonstrate that our approach significantly improves multi-view stylistic consistency and produces stable, expressive 3D stylizations while preserving the core semantic structure of the scene.