Zoned Namespace (ZNS) defines a new abstraction for host software to flexibly manage storage in flash-based SSDs as append-only zones. It also provides a Zone Append primitive to further boost the write performance of ZNS SSDs by exploiting intra-zone parallelism. However, making Zone Append effective for reliable and scalable storage, in the form of a RAID array of multiple ZNS SSDs, is non-trivial, since Zone Append offloads address management to ZNS SSDs and requires hosts to specifically manage RAID stripes across multiple drives. We propose ZapRAID, a high-performance log-structured RAID system for ZNS SSDs by carefully exploiting Zone Append to achieve high write parallelism and lightweight stripe management. ZapRAID adopts a group-based data layout with a coarse-grained ordering across multiple groups of stripes, such that it can use small-size metadata for stripe management on a per-group basis under Zone Append. It further adopts hybrid data management to simultaneously achieve intra-zone and inter-zone parallelism through a careful combination of both Zone Write and Zone Append primitives. We implement ZapRAID as a user-space block device, and evaluate ZapRAID using microbenchmarks, trace-driven experiments, and real-application experiments. Our evaluation results show that ZapRAID achieves high write throughput and maintains high performance in normal reads, degraded reads, crash recovery, and full-drive recovery.