This study addresses path planning for multi-slot mobile robots performing mixed return–picking operations in intelligent warehouses. In these scenarios, task sequences are constrained by slot occupancy, while conventional MAPF methods provide limited task-specific guidance for neighborhood selection and inadequately represent turning and waiting costs in local replanning. To address these issues, an improved MAPF-LNS2 algorithm is proposed. A centralized MAPF model is formulated with slot states, task types, and precedence constraints. The algorithm combines task-state-priority neighborhood selection, slot-feasible initial mixed-task planning, and an improved SIPPS replanner with behavior-based costs and adaptive soft-conflict penalties. Task-sequence feasibility and the monotonic non-increase of conflict counts are also analyzed. Experiments show that the mixed picking strategy reduces the total system path length by 14.79% on average. Compared with PBS, ECBS, CCBS, CPLNS, and the original MAPF-LNS2, the proposed method achieves shorter task completion times and total path lengths in most scenarios. The average task completion time is reduced by 55.32% and 52.74% relative to PBS and ECBS, respectively. Moreover, all 20 trials were successfully solved in the high-load scenario, demonstrating the effectiveness and scalability of the proposed method in medium- and large-scale multi-slot warehouse environments.