In expert-parallel (EP) MoE serving, every layer synchronizes at the slowest GPU. Dispatchers balance token counts (EPLB, LPLB, UltraEP) or activated-expert counts (METRO), assuming expert time is linear in one. Measurements on two datacenter GPU generations show it is neither: below \nstar≈156--168 tokens, HBM weight streaming dominates---cost attaches to \emph{activated replicas}, not tokens; above it, grouped GEMM rounds tokens to 128-tile M-tiles, so \emph{splitting} an expert adds padded compute. A max-affine profile t=max(a+bG,c+βN) captures both regimes. Realistic decode batches hold hot experts in the linear regime and cold in the flat \emph{simultaneously}; recorded batches show proxy dispatches differ by 1.4--1.6× in modeled block time (p95 up to 1.7×), and \emph{which} proxy wins flips with the regime. We formalize per-batch dispatch as a fixed-charge makespan problem---NP-hard on two fully replicated GPUs, polynomial in degenerate limits---and present \sys{}, a makespan-aware dispatcher solving it in milliseconds off the critical path; its SGLang integration runs out-of-process and fuses dispatch with count collection into one in-graph kernel. Anchored by an 8-GPU TestbedA microbenchmark, \sys{} stays within 1% of the best fixed baseline everywhere and wins by up to 15.5% where regimes mix. End-to-end on TestbedB, Qwen3-235B (inside the win region) gains 4--6% throughput and cuts p99 latency by ∼15.6%; DeepSeek-V3 (outside, communication-dominated) shows only mechanism cost. A phase diagram, not a universal win, is the claim: it predicts both outcomes before deployment.