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It is common to prove by reasoning over source code that programs do not leak sensitive data. But doing so leaves a gap between reasoning and reality that can only be filled by accounting for the behaviour of the compiler. This task is complicated when programs enforce value-dependent information-flow security properties (in which classification of locations can vary depending on values in other locations) and complicated further when programs exploit shared-variable concurrency. Prior work has formally defined a notion of concurrency-aware refinement for preserving value-dependent security properties. However, that notion is considerably more complex than standard refinement definitions typically applied in the verification of semantics preservation by compilers. To date it remains unclear whether it can be applied to a realistic compiler, because there exist no general decomposition principles for separating it into smaller, more familiar, proof obligations. In this work, we provide such a decomposition principle, which we show can almost halve the complexity of proving secure refinement. Further, we demonstrate its applicability to secure compilation, by proving in Isabelle/HOL the preservation of value-dependent security by a proof-of-concept compiler from an imperative While language to a generic RISC-style assembly language, for programs with shared-memory concurrency mediated by locking primitives. Finally, we execute our compiler in Isabelle on a While language model of the Cross Domain Desktop Compositor, demonstrating to our knowledge the first use of a compiler verification result to carry an information-flow security property down to the assembly-level model of a non-trivial concurrent program.