I've been following this
thread for a couple of days now, and its of interest to me because in principle (or in theory) I love beavers. I love the idea of them repopulating North America to the fullness of their former range. I love what they do to the hydrology of watershed when allowed to build their dams, ponds and channels.
But in reality, I've never had to deal with them. I know that they can be tremendously difficult to co-exist with because they deforest everything around them, flood what used to be farmable, and in general, busy themselves with all manner of activities that humans find destructive.
30 years ago, I had an Uncle in Edmonton who had an acreage outside of town next to a small creek. Beavers took up residence and soon had dammed the creek and created a lovely pond. Everyone loved it. They were cute and industrious and we had a place to skate in the winter. Soon they'd cleared out all the poplar trees, then the birch, then they cut down the spruce trees which everyone said they wouldn't because they didn't like spruce. They were huge—about 3 feet long and 60 or 70 lbs. They'd graze on the grass at night like
cattle. Eventually, they were dragging trees over 200 yards from the other side of the house, all the way over the
lawn and garden, and down to the river. In the course of one week, they took almost all of his entire orchard of apples, plums, cherries, apricots and apples. That's when my Uncle finally put a stop to it.
He "eliminated" the beavers and took an excavator to the dam. I was sad to see the beavers go.
The difficulty is coexistence. We are finding this true about many wild animals.
Deer have breed without preditors for so many decades that they are now a threat to motorists, and a bane to gardeners everywhere. And because there are so many deer now, mountain lions are making a huge comeback (good) and starting to populate areas where they have frequent encounters with humans (not good). In our area we have coyotes that are brazen and unafraid of humans. They stroll through my backyard and freak my
chickens out. The interface between habitat for animals and habitat for humans is now fuzzier than ever before.
Best of luck to you as you seek ways to coexist. Perhaps, in the end, relocating them to a place where they will be welcome would be best. I'd hate to see you employ the same "solution" my uncle did.