"it depends on the state of the battery." Just after starting it will charge 5 or 7 amps. After that it will hover on the + side of 0. This sounds like proper operation. After starting, the battery voltage will drop, and the regulator will increase the current until the battery voltage comes up to the proper voltage which should be about 7 volts.
"Reving the engine wide open reduced discharge to near 0." This indicates that the generator is too small for this application, and/or that the RPM of the generator is too low. When you speed up the motor, and the generator still can't quite keep up with the load, it indicates the generator is too small.
Try this. With the engine running and the voltage set to 7 volts with the lights off, turn the lights on and see if you see arcing of the contacts of the voltage regulating relay. You can also use a screwdriver to short the contacts and see if the voltage comes up. If the voltage doesn't change with the contacts shorted, the generator is putting out all it can. You can then rev the motor up and short the contacts again to discover what happens with more RPM.
Let me explain the limitation of these mechanical regulators. Realize I am an expert on servos and feedback control devices.
The regulator does not have infinite gain, so as you increase the load on the generator, the voltage will drop somewhat. It appears that the generator is too small for this application, and so when the current command increases, the generator and regulator cannot keep the voltage constant.