I have seen the same thing buddy. I try to return them to the woods. A couple years ago we killed a pair, and left them lay out in the high grass where we killed them. Went back in the fall, and they were still in the field looked about the exact same just deflated to a flat look. If I had a machine I would just dig a hole and bury it over a few times a year.
I know a guy who does the creek thing too..