Hi Pooh Bear,
On your T-111, find some exterior oil base or latex paint and slather it on the wood. Spray, roller or brush the paint on, just make sure you get lots of paint on the edges and in any cracks or seams on the wood. The more coats the better. The point is that the paint will block water from getting inside the plywood layers where it will start to decompose the wood cell fibers. "Dry rot" is not dry, it should rightfully be called "wet rot".
Note- on any piece of milled lumber, where a cut is made across the grain, as in lumber used for a flat-bed trailer, the ends of the planks will last years longer if paint is applied on the cut end until the wood can't soak it up anymore. That is why the ends of lumber left outside rot first, because that is where the rain or ground water is soaked up first.
Old carpenter wisdom.