GREASE!
Petroleum jelly will gum up everything in no time, has no high pressure properties, is messy, and is not meant for machinery. A tube of white lithium grease can be found at any hardware store for cheap, and will be much better suited for Zamak gears.
I have used white lithium grease on Zamak and never had a problem. The lithium metal in the grease adheres to the gear face and really keeps wear down. Try to get one with Teflon.