I'll tell you what does work very well- 8 hour liquid paraffin cells. These are the exact same diameter as the little tea light candles that those lanterns are made to run on, but they burn 8 hours or so. I've never seen one leak (they're pretty tightly capped) and unlike a regular candle they can be snuffed and relit as many times as you like so long as there's still fuel. As a chef I've used them for decades in restaurants- they're the candles used in the little lamps on your table.

In my experience they work great in the UCO Mini lantern. They work great as a light source and there's no wax to spill. Liquid paraffin is another term for a refined type of kerosene. As an added bonus, they work great as a firestarter. It's easy to light the wick and they burn long enough to get about anything going.