In stroke-based rendering, search methods often get trapped in local minima due to discrete stroke placement, while differentiable optimizers lack structural awareness and produce unstructured layouts. To bridge this gap, we propose a dual representation that couples discrete polylines with continuous Bézier control points via a bidirectional mapping mechanism. This enables collaborative optimization: local gradients refine global stroke structures, while content-aware stroke proposals help escape poor local optima. Our representation further supports Gaussian-splatting-inspired initialization, enabling highly parallel stroke optimization across the image. Experiments show that our approach reduces the number of strokes by 30-50%, achieves more structurally coherent layouts, and improves reconstruction quality, while cutting optimization time by 30-40% compared to existing differentiable vectorization methods.