We live in an area where it rains alot so using any type of absorbant bedding just creates a boggy stinky mess. We have to keep our ground clear of leaves, grass clippings, etc. in order to allow the rain water to absorb into the ground rather than soaking into absorbant materials that hold moisture and manure like a sponge above the ground where it squishes when we walk over it.
As long as the poop is liquid enough to soak into the ground without getting trapped above ground, you will have clean dirt and your grass will grow lush and beautiful. Since you already have the grass, all you have to do is rinse it with water to liquify the poop and feed the grass and the worms. Our grass gets washed off by the rain all winter but in the summer we water it with the hose in order to keep the grass clean. I personally think grass is ideal for ducks because they will trim it and keep it healthy looking as long as they are not confined to an area that is too small that the manure builds up too deep on top of the grass.
We use shavings inside the chicken coops and we hose out their yard the same way we do with the ducks but it takes far more cleaning and their manure will burn the grass while duck manure is not hot like chicken manure. We can't use our shavings as mulch with chicken manure in them due to the smell when it gets wet so it goes in our yard waste to be picked up with our garbage. They take too long to compost so we just have them removed.
If you water down your duck poop so it absorbs into the ground, you will grow a healthy worm population below the grass that will eat up the poop and give you worm casings in return for a nice rich topsoil. I think you have an ideal situation if you just add water.
