Static-graph LLM decoders provide predictable launches, fixed tensor shapes, and low submission overhead, but online decoding exposes highly irregular KV-cache behavior: request lengths differ, EOS events arrive asynchronously, and logical histories fragment over time. Dynamic runtimes recover flexibility through paged KV management and step-level scheduling, while static-graph executors often over-reserve memory and suffer burst-time latency outliers. This paper studies whether much of this variability can be absorbed below a fixed decode interface. We present KV-RM, a runtime design that regularizes KV-cache movement beneath a static-graph LLM decoder. KV-RM decouples logical KV histories from physical storage, tracks active KV state through a block pager, and materializes each decode step through a single committed descriptor. A merge-staged transport path coalesces non-contiguous KV mappings into a small number of large transfer groups before a fixed-shape attention kernel consumes them. Optional bounded far-history summaries can be enabled under the same interface, but the core design does not depend on them. On a 2-GPU NVIDIA A100 node, KV-RM improves mixed-length decoding throughput and tail latency relative to a static-graph baseline, reduces reserved KV memory across workload families, and removes severe burst-time latency spikes under production-trace replay. These results suggest that KV-cache movement, rather than kernel shape, can be an effective boundary for recovering runtime flexibility in static-graph LLM serving.