Best way to preserve excess tallow long-term
You can freeze tallow.  Dehydration and the freeze-thaw cycle of home freezers are the enemies of long term storage.  You can't stop the freeze-thaw cycle, but if you minimize exposure to dehydration (freezer burn) by storing full containers, or even vacuum packing, you can keep them that way for quite a while.

You added a picture, which is helpful.  I might not freeze glass jars.  You could risk expansion and breakage.