Oblivious RAM protocols (ORAMs) allow a client to access data from an untrusted storage device without revealing the access patterns. Typically, the ORAM adversary can observe both read and write accesses. Write-only ORAMs target a more practical, {\em multi-snapshot adversary} only monitoring client writes -- typical for plausible deniability and censorship-resilient systems. This allows write-only ORAMs to achieve significantly-better asymptotic performance. However, these apparent gains do not materialize in real deployments primarily due to the random data placement strategies used to break correlations between logical and physical namespaces, a required property for write access privacy. Random access performs poorly on both rotational disks and SSDs (often increasing wear significantly, and interfering with wear-leveling mechanisms). In this work, we introduce SqORAM, a new locality-preserving write-only ORAM that preserves write access privacy without requiring random data access. Data blocks close to each other in the logical domain land in close proximity on the physical media. Importantly, SqORAM maintains this data locality property over time, significantly increasing read throughput. A full Linux kernel-level implementation of SqORAM is 100x faster than non locality-preserving solutions for standard workloads and is 60-100% faster than the state-of-the-art for typical file system workloads.