Whatever other plants you put by ducks, I would say stick with plants that are taller than they can reach and woody. Trees, shrubs and bushes worth well. Cacti might work for you. Not sure if a duck would get stuck with thorns though so avoid any that are toxic.I moved the pool out there and placed the olive tree where I want it. Maybe that will jump start something.
I’m trying to figure out what else to put out there once the lilac and olive grow up.
My biggest issue with ducks are poop and mud. And those two mix together always to form the nastiest sludge. You may be much drier in AZ than I am though. My duck run is currently an outdoor deep litter bed of sorts with leaves, straw and wood chips that I'll muck out next year into the compost bins and refill with whatever carbon rich matter I can at that time. Needless to say, it isn't a pretty area with lush greenery. I intend to plant flowers in front of the run fence and would like to plant a short tree in the center of their run. The nutrient soil and water would feed a tree well that didn't mind wet roots. That's my vision for now... gardening a duck run isn't an easy task.