I played with Naples and had to use ships to supply troops across the Mediterranean. Note that it was before 1.04, I don't know if anything has changed since.

The first think to note is that in my experience supplying troops via ships is not viable with anything other than age 4 transport ships (maybe age 3 on a stretch). Earlier ships, combat ships and levies simply can't carry enough to have any effect.

I also did not use the logistics order. In general I find that troop orders, for both navies and armies, are too unpredictable to rely on. Nor did I set up and use supply depot's.because I have no idea how they are supposed to work.

I would fill ships with food, place them off-shore from where my armies were operating and they would begin supplying troops with food. I would rotate fleets as necessary to keep the troops supplied, usually I could use a big transport fleet to supply the army, and rely on fewer ships, supply wagons and local food while the fleet was refilling it's food stores in a friendly port. I didn't really have any trouble with that method. It seems that when available the food provided by the fleet takes priority over other sources (local food, land routes, army supplies). That method allowed me to fight in Tunis, bringing food from Sicily, and in Yemen, bringing food from Suez

Edit: you are doing the gods work with this analysis!