Ok so Im on 2.5 acres.. I have had mom, dad and little ones... as well as the neighbors geese, 6 to 8 of them. I havent had a problem with stink, really. My pen is just about 16x16. My gander died as did my tom after a really bad respiritory infection went through my birds, 3 yrs ago. I moved the mom turkey in with mom goose and they have been keeping each other company for the past 3 yrs... Geese are actually cleaner than chickens ... their nesting area where they lay their eggs is never pooped in.. the chickens poop everywhere they go... I keep a swimming pool in the goose pen for the warm summers so they can swim and bathe. I also give them a bucket of warm water to wash their faces in every evening even if it is 30 below. They need to wash off their eyes or they cant see. To keep the stink down I cover their pen bottom with straw. It meshes with the poop and helps compost it... I also mix green grass clippings and hay. I do that in the chicken pen, and dog lot also with very little to no smell. The only time I really have a bad smell is when I let it go to long.
As far as the pool they wash in it and I empty and refill it as it gets dirty. If you have them in a pond, I can see where that will stink over time...
I agree you dont want one goose. They mate for life and will defend their mates to the death. I actually thought my female would die when the male did. She didnt and she is still very healthy.