Abstract: To address the strict sequencing requirements imposed by the rebar plane stability in automated rebar-tying operations, this study formulates an order-constrained full-coverage path planning (OC-CPP) problem. To solve this problem, a sequence-aware full-coverage path planning method is proposed that integrates a priority-aware neural network (PANN) with a dead-zone escape strategy based on A* (DZES-A*). The objective is to achieve rebar plane coverage planning with high stability, fully executable paths, and low repetition rates. First, the obstacle regions on the rebar plane are expanded according to the obstacle types, boundary constraints, and structural dimensions of the tying robot. This enables the effective avoidance of potential collisions during planning. Then, the expanded environment is discretized into grid cells based on the effective workspace of the robot to construct a grid map suitable for full-coverage path planning algorithms. Considering the practical engineering requirement that the edge regions of the rebar mesh should be tied before the center to reduce the cumulative displacement and enhance the overall plane stability, the planned paths must also satisfy the motion feasibility under obstacle avoidance and robot structural constraints. To satisfy these requirements, a target-reconstruction-based PANN strategy is proposed. This strategy incorporates a tying-priority matrix and cross-domain inhibition mechanism, enabling the planning process to comply with sequence constraints, adapt to environmental conditions, and achieve full coverage. In addition, a target reconfiguration strategy (TRS) is applied to map the eight-neighborhood environmental information into four-neighborhood executable actions without losing environmental details, ensuring that the planned paths are feasible and executable by the robot. Because of the edge-to-center sequence constraint, the planned paths may become trapped in the dead zones. To address this issue, the A* algorithm is integrated into the coverage framework to generate feasible escape paths. Furthermore, a DZES-A* mechanism is introduced to balance the feasibility and efficiency of the escape segments. The resulting DZES-A* paths can be seamlessly integrated into the overall coverage trajectory to produce a complete, sequential, and executable full-coverage plan. To evaluate the performance of the proposed method in practical rebar-tying operations, a comprehensive evaluation system was established including the rebar plane stability, coverage rate, and repetition rate. Plane stability was quantified using a disturbance diffusion–dissipation model that reflected global structural stability by analyzing the propagation and attenuation of disturbance energy across the plane. To verify its robustness and superiority, multiple two-dimensional comparative experiments were conducted. Zigzag scanning, a traditional bio-inspired neural network (BINN), and the proposed PANN were each combined with both classical A* and DZES-A* algorithms to systematically assess the performance under different planning frameworks. The results indicated that, compared with classical A* that might generate non-executable escape paths, all escape paths generated by DZES-A* were fully executable. When the coverage rate was maintained at 92.92%, the PANN method reduced the repetition rate by 1.28% and 0.27% compared with zigzag scanning and the standard BINN, respectively, while increasing the computation time by only 0.01 s and 0.21 s, respectively; the rebar plane stability improved by 31.96% and 42.56%, respectively, significantly enhancing the overall structural performance. Finally, experiments conducted on a laboratory rebar-tying robot under multiple scenarios demonstrated the generality, stability, and engineering feasibility of the proposed method in automated rebar-tying operations.