Autonomous LLM agents fail because long-horizon policy remains implicit in model weights and transcripts, while safety is retrofitted post hoc. We propose Traversal-as-Policy: distill sandboxed OpenHands execution logs into a single executable Gated Behavior Tree (GBT) and treat tree traversal -- rather than unconstrained generation -- as the control policy whenever a task is in coverage. Each node encodes a state-conditioned action macro mined and merge-checked from successful trajectories; macros implicated by unsafe traces attach deterministic pre-execution gates over structured tool context and bounded history, updated under experience-grounded monotonicity so previously rejected unsafe contexts cannot be re-admitted. At runtime, a lightweight traverser matches the base model's intent to child macros, executes one macro at a time under global and node-local gating, and when stalled performs risk-aware shortest-path recovery to a feasible success leaf; the visited path forms a compact spine memory that replaces transcript replay. Evaluated in a unified OpenHands sandbox on 15+ software, web, reasoning, and safety/security benchmarks, GBT improves success while driving violations toward zero and reducing cost. On SWE-bench Verified (Protocol A, 500 issues), GBT-SE raises success from 34.6% to 73.6%, reduces violations from 2.8% to 0.2%, and cuts token/character usage from 208k/820k to 126k/490k; with the same distilled tree, 8B executors more than double success on SWE-bench Verified (14.0%58.8%) and WebArena (9.1%37.3%).