Sparse anchors provide a compact interface for human motion authoring: users specify a few root positions, planar trajectory samples, or body-point targets, while the system synthesizes the full-body motion that completes the under-specified intent. We present AnchorRoute, a sparse-anchor motion synthesis framework that uses anchors as a shared scaffold for both generation and refinement. Before generation, AnchorRoute converts sparse anchors into anchor-condition features and injects the resulting condition memory into a frozen Transition Masked Diffusion prior through AnchorKV and dual-context conditioning. This preserves the generation quality of the pretrained text-to-motion prior while learning sparse spatial control. After generation, the same anchors are evaluated as residuals: their timestamps define refinement intervals, and their residuals determine where correction should be concentrated. RouteSolver then refines the motion by projecting soft-token updates onto anchor-defined piecewise-affine interval bases. This couples generation-time anchor conditioning with residual-routed refinement under one anchor scaffold. AnchorRoute supports root-3D, planar-root, and body-point control within the same formulation. In benchmark evaluations, AnchorRoute outperforms prior sparse-control methods under the sparse keyjoint protocol and consistently improves anchor adherence across control families. The results show that the learned anchor-conditioned generator and RouteSolver refinement are complementary: the generator preserves text-motion quality, while RouteSolver provides a controllable path toward stronger anchor adherence.