Hi Charley
You're right as far as I see. You could run down to Cuba "for" sugar or run from Cuba "with" a load of sugar. The middle passage of the slave trade would have slavers running down to Cuba with slaves, running to New England with sugar or molasses then running to England (or elsewhere) & then completing the circle by running back down to Africa. This would be the North Alantic circle route, following the trade winds (& the gulf stream) or running before the (trade)winds or running downwind with the wind at your back. The other triangle route was Europe (or England, hence limejuice squeezer) to Africa to West Indies & finally back to Europe. Even if this is not refering to any leg of the slave trade, Cuba along with the many other islands of the area were the producers of sugar so the verse with "load the sugar & homeward go" would make more sense to me than the rest. Unless they're (the ship) loaded with sugar & running down though the next leg of the circle that would eventually bring them back to Cuba (not likely I think). Musically Running down "FROM" Cuba would be as singable as "TO". Not much help as far as clearing this up for you, maybe someone with a better grasp of the running down or the song's history will do you better.
Better luck Charley, Barry