Accurate document parsing requires both robust content recognition and a stable parser interface. In explicit Document Layout Analysis (DLA) pipelines, downstream parsers do not consume the full detector output. Instead, they operate on a retained and serialized set of layout instances. However, on dense pages with overlapping regions and ambiguous boundaries, unstable layout hypotheses can make the retained instance set inconsistent with its parser input order, leading to severe downstream parsing errors. To address this issue, we introduce a lightweight structural refinement stage between a DETR-style detector and the parser to stabilize the parser interface. Treating raw detector outputs as a compact hypothesis pool, the proposed module performs set-level reasoning over query features, semantic cues, box geometry, and visual evidence. From a shared refined structural state, it jointly determines instance retention, refines box localization, and predicts parser input order before handoff. We further introduce retention-oriented supervision and a difficulty-aware ordering objective to better align the retained instance set and its order with the final parser input, especially on structurally complex pages. Extensive experiments on public benchmarks show that our method consistently improves page-level layout quality. When integrated into a standard end-to-end parsing pipeline, the stabilized parser interface also substantially reduces sequence mismatch, achieving a Reading Order Edit of 0.024 on OmniDocBench.