WebGIS development requires rigor, yet agentic AI frequently fails due to five large language model (LLM) limitations: context constraints, cross-session forgetting, stochasticity, instruction failure, and adaptation rigidity. We propose a dual-helix governance framework reframing these challenges as structural governance problems that model capacity alone cannot resolve. We implement the framework as a 3-track architecture (Knowledge, Behavior, Skills) that uses a knowledge graph substrate to stabilize execution by externalizing domain facts and enforcing executable protocols, complemented by a self-learning cycle for autonomous knowledge growth. Applying this to the FutureShorelines WebGIS tool, a governed agent refactored a 2,265-line monolithic codebase into modular ES6 components. Results demonstrated a 51\% reduction in cyclomatic complexity and a 7-point increase in maintainability index. A comparative experiment against a zero-shot LLM confirms that externalized governance, not just model capability, drives operational reliability in geospatial engineering. This approach is implemented in the open-source AgentLoom governance toolkit.