A battery doesn't mean anything when doing DC. It is just a storage unit, it doesn't have to be there and nothing will change.
Follow that link I gave, it shows how to float the ground. You can hook up the rectifier to the wiring wiring harness, just needs to hook up to the correct wires from the stator.
The stator produces the AC power, just need a rectifier to convert to DC.
See below, just ignore the relay and breaker.