Do one thing at a time - . You can try a little white lithium grease on the gear after cleaning off the old grease, or 3 in 1 oil on the pulley, but more often I find it's the motor that makes the noise. If it's the motor, just replace it. If oiling the pulley reduces the noise, plan on replacing them soon. If lubing the gear helps, inspect for wear, cracks or debris in the teeth that you may have missed when cleaning the gear.
BTW, my son and daughter in law are down in Australia on vacation. They're having a lot of fun down there.
Good Luck