Is it possible this is not an electrical problem. If the engine dies as soon as the generator tries to pick up the electrical load, it might point to a fuel delivery problem. When running unloaded, the engine needs very little fuel so it appears to run OK. As soon as the generator starts to feed power to electrical system, the engine power needs to increase proportionally. Howerver, if there is not enough fuel getting to the engine, the RPM will fall and the engine will either stop on it's own or possibly shut down automatically on low voltage and/or low frequency.
