sorry if this don't fit your situation don't know without being there I have muscovies they are real quite I have them in moveable pens that are 4 ft /10 ft the pens could be any size you want your garden.put them were you want to garden and take care of them . after the grass is gone add straw or your bag from your baggier mower to compensate for all the nitrogen that is going down deep in the ground after the grass is visible gone the straw /leaves/grass clippings will absorb any smell they might have.
give them a lot of water to work with they will relive the soil of grass at that spot and not turn soil over to much add any
compost or such that you want they will spread it and poop on it when you get the layer about 4 inches thick or how thick you want it move them to the next spot.you do need to keep them on the spot at least 1 month.You can also put red worms in that spot after the ducks are moved and they will go to work neutralizing the soil . you will need some kind of barrier to keep the grass out or it will just come back.
My favorite thing to plant first is corn which will take a lot of nitrogen but returns a lot to he soil if you put the stalks on the soil as ground cover when they are done.
some times people just have to garden .