Zoned Namespace (ZNS) SSDs offer compelling advantages over conventional SSDs by exposing a zoned storage interface that helps mitigate write amplification and improve performance. However, their strict sequential-write constraint within each zone poses a significant challenge for many real-world applications that naturally generate out-of-order write requests. Unaligned or out-of-order writes in ZNS can trigger costly read-modify-write operations or command rejections, leading to severe performance degradation. To address this issue, this paper proposes Z-STREAM, a novel, two-level collaborative scheduler. The first level is a lightweight host-side batch sorter (HBS), implemented in the NVMe driver path, which intercepts and reorders I/O requests within small batches based on their logical block addresses. The second level is the device-side compensating write set engine (CWS-Engine), a transparent reordering engine within the ZNS firmware. The CWS-Engine utilizes a per-zone software buffer to absorb out-of-order writes. When writes are evicted from this buffer, the engine generates persistent metadata for a novel structure we term the compensating write set (CWS). CWS metadata, efficiently managed by a dedicated binary search tree (BST), ensures correct data retrieval during read operations while minimizing performance overhead. We have implemented and integrated this entire collaborative architecture into the FEMU simulator. Our evaluation demonstrates that the proposed system potently and transparently transforms chaotic write streams into ZNS-compliant sequential writes, reducing write amplification to a near-ideal 1.003 and improving throughput by up to 3.82x on representative workloads.