Neural solvers for the Flexible Job-Shop Scheduling Problem (FJSP) typically refresh graph representations and update feasibility after every operation--machine decision. However, only feasibility must remain exact at every step, whereas graph encoding is substantially more expensive and can potentially be refreshed less frequently. We present CoRS, which decouples them: an interval-level graph representation is reused across multiple sequential decisions, while a stepwise feasibility state is updated after every action. This two-timescale design amortizes graph encoding without parallelizing action generation or relaxing scheduling constraints. CoRS further develops a feasibility-preserving composite-interval decoding scheme with dynamic constraint tracking and boundary state synchronization, which reduces representation refresh frequency while maintaining continuous feasible schedule construction. Furthermore, to alleviate representation staleness caused by interval-level state reuse, CoRS introduces enhanced static features as a compensation mechanism. By providing more comprehensive structural information of the scheduling problem, these features improve the model's perception of overall problem characteristics. Extensive experiments on synthetic and multiple public FJSP benchmarks demonstrate that CoRS significantly reduces inference time while maintaining competitive solution quality, achieving favorable speed-quality trade-offs under tight wall-clock budgets and low-latency scenarios.

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