Proper ground is necessary on products requiring external connection. Siz eof the ground is based on the size of the unit.
300 watts would not require much over a #14 ground. Memeory says the ground is 12.5 % of the max rating of the device.
I would run a separate ground and not tap onto any existing grounds. Those grounds would (should) have been calculated on the loads originally connected.
I just went to website and looked at manual for the unit. The designer sure wants oversized wiring for DC power and ground. They advise #4 for ground, min #6 for power and fused at 100 amps. This seems exremely high for the 3 amp 120 volt output.
Manual
