Well, I've talked to most of the neighbours over the weekend; everyone seems sincerely dismayed and some have offered to help (dragging bodies out of stream) which is nice.
As it turns out, some of the dumps may be a bit older than I initially thought - a sheep lying upright underwater looks quite intact until you pull it over, and I don't really have any idea how long it takes them to rot underwater in winter. Still, at lease those were easier to drag out than the recent ones. Dead waterlogged sheep are HEAVY.
Will call EA once I've got rid of them.
m