I strongly support the use of an oil that has a high temp rating and will not attack plastic.
If you can handle it, make a cover for the gearbox assembly to keep dirt and other debris off PLUS, install some sponge material at the axle hole and poke the axle shaft through it. This keep dirt from entering at that area.
Remember, grease will attract dirt and is more difficult to clean off than oil, so oiling periodically is better than one application with grease which is more suited for roadwheels and idlers where it's a sealed system.
Jeff