Spraying borax can suppress mold quite a bit.
Waxing the lids can prevent rusting.
What provisions do you have for airflow?
A
solar chimney up the south side of the canning shed,combined with a perforated black drain pipe earth tube for incoming air, might provide temp and humidity moderated airflow.
Any
water coming from above that point might pool on top of the plastic, causing other problems.
An easily removed walking surface could allow easier changes, so if you try the vapor barrier on the floor, maybe cover it with pavers and sand at first.
Sealing the walls with a waterproofing paint might help as well.
Does water condense on the plywood ceiling?
If so, I would insulate there.