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A user's approval-workflow flowchart came out with the return arrow drawn straight through two unrelated steps, and a second report showed arrows leaving a box and bending straight back across it. Measured over 250 generated flowcharts (2722 edges): 347 arrows crossed an unrelated box and 215 waypoints landed inside a shape. Four defects, each measured in isolation: 1. The invisible layer containers draw_graph emits were handed to the router as frames, so every clean return path was rejected for "trespassing" on a border that is not drawn, and the fallback cut through two boxes. Excluding invisible containers: 347 -> 218 crossing arrows, no diagram made worse. 2. The router chose the horizontal-vs-vertical axis BEFORE searching, so when the only clean corridor ran along the other axis it was never looked at. A complete two-bend candidate generator that tries both trunk axes, all four sides at each end, and the port fractions: 218 -> 27. (An independent ablation measured the axis pre-choice alone at a 40% per-edge failure rate.) 3. Nothing stopped a route's first leg from turning back across its own source shape - the obstacle test exempts an edge's own endpoints, and must, since the line has to touch them. A terminal-leg rule refuses such routes outright: 215 -> 4 hooks. 4. A two-bend search cannot express the staircase needed when a box sits directly between two vertically aligned nodes (21 of the last 27 crossings). Added the orthogonal visibility graph + A* from Wybrow, Marriott & Stuckey, "Orthogonal Connector Routing" (GD 2009) - the libavoid algorithm - as the backstop when the candidate search finds nothing. The interesting-points grid is provably sufficient: any valid route shrinks onto it without getting longer or gaining bends. The A* state is (point, incoming direction) with libavoid's bend cost of 10, and the admissible bends-remaining heuristic, so it returns a cheapest route, not merely a route. Implemented from the paper, not ported. After all four: 0 crossing arrows and 0 hooks over the same 250 diagrams, page area unchanged (494k px^2 mean), 260ms for the whole corpus, mean 0.82 bends per edge. The shape ladder still runs first, so routes that were already clean are byte-identical. Also post-nudge validation now checks the whole path (the nudge pass only reverts the single segment it moved, judged in isolation) and restores the search's route if nudging made it dirty.