Most LLM-driven GIS assistants solve narrow single-step tasks tightly coupled to proprietary platforms such as ArcGIS or QGIS, limiting their use for the multi-step, cross-format pipelines that define professional geospatial analysis. We present GISclaw, a comprehensive open-source agent system that performs realistic GIS analysis end to end - spatial joins, raster algebra, kriging interpolation, machine-learning classification, network analysis, choropleth cartography - directly through Python with no commercial GIS dependency. GISclaw couples an LLM reasoning core with a persistent Python sandbox pre-loaded with the open-source geospatial stack, three engineered prompt rules (Schema Analysis, Package Constraint, Domain Knowledge Injection), and an Error-Memory module for self-correction. A single backend-agnostic architecture supports both cloud-API and locally deployed open-weight LLM backends, enabling air-gapped deployment without loss of capability. On GeoAnalystBench - 50 expert-curated multi-step tasks averaging 5.8 analytical steps across vector, raster, and tabular data - GISclaw reaches up to 100% task success and 97% mean success over three independent runs. We further conduct 1,800 controlled experiments (50 tasks x 6 backends x 2 architectures x 3 repeats) with bootstrap 95% CIs, paired Wilcoxon tests, and a composite-score sensitivity analysis (Kendall's tau median = 0.94), and introduce a three-layer evaluation protocol combining code structure, reasoning process, and type-specific output verification. The Single-Agent ReAct loop reliably outperforms the Dual-Agent Plan-Execute-Replan pipeline on every cloud backend (Cliff's delta = 0.15-0.41); only the locally deployed 14B model gains from multi-agent orchestration, suggesting architectural complexity should match model capability rather than be added by default.