Maybe you can distract them by poking some holes in their downstream dam. Or install an inflatable bear. I bet the giant Easter bunny ones are on sale now.
They are persistent creatures. I have a friend who has trapped some out for me from time to time. I don’t know if he eats them. He does eat game pretty exclusively. Hunts for deer and turkey certainly, a fair amount of bear. He works for DEEP, so has access to meat from nuisance bear or roadkills. I have another friend who travels to hunt, also eats bear he hunts in Maine, other animals that one wouldn’t hunt here.
I have no problem with the downstream beavers. It's the dam at the driveway culvert causing concern. Water went over the top of the drive 10 years ago during Irene and washed out a good chunk. The original culvert for the driveway has long collapsed and I'm relying on 2 backup ones installed at a higher elevation, including a 36" one I put in after the flood. Could not put it in at stream elevation or would have needed a state permit, which in turn would make it sized for a 500 year flood with no backup of the water. That means an 8 or 10' culvert, arch or bridge and much $$'s. If current battle continues I may do exactly that.
The problem with those guys is that they are absolutely adverse to compromise. I have places I would be happy to have them play if they would stay away from places I care about.
If they stop munching on the ash and move into the sugar maples, we'll have a serious confrontation. They seem to prefer the ash, however, which is fine since those are all doomed by the ash borer.
Here they mostly like birch, especially yellow birch, although occasionally they get into something more resistant, even the occasional oak. I find the flooding more annoying than the chewing.