Low-overlap indoor RGB-D point cloud registration remains vulnerable to hard failures because robust recovery and deployment latency are rarely achieved by one registrar. We present a budget-aware rescue-routing framework that keeps PointDSC+FCGF as the fast primary path and separates deployable pre-rescue gates from frozen-candidate selector analysis. On 3DLoMatch, the frozen selector DRACO-Stack reaches strict success of 0.5205 vs. 0.4278 for PointDSC+FCGF, while the deployable DRACO-Gate reaches 0.4801; a matched accuracy-only CoFiNet reconstruction on the same 1781 pairs reaches 0.5390. On 3DMatch, DRACO-Route activates 369/1623 pairs and reaches 0.8885 at 721.18 ms, compared with 0.8694 for PointDSC+FCGF and 0.9082 at 8310.48 ms for always-on RegTR. Redwood is used as public-transfer validation, where PointDSC+FCGF reaches 0.1425 vs. 0.1043 for PointDSC+FPFH. The results support selective indoor hard-tail rescue under an explicit runtime budget, without claiming a universal scene-free router or a new backbone.