Good luck on the hunting , eliminate every one . If they like your pond , and are content in the dens , I don't know how far they'll drag branches to store for this winters food . That or with entrances exposed , with low water , to den if they'll even stick around , but when rains finally come , they may remember what a wonderful home it was and return , I'd be eliminating the Bucktoothed Rats before they decide dam is too their liking .
I only have one, I hope. This is Florida I can't trap, shoot or harm a beaver without a permit. I must go through the county bureaucrats to get the permit & then a state trapper eliminates the varmint perhaps. It comes & goes. I will not see it for 4 months & then it is back. Can't figure out how it has stayed around so long because of limited food. Cleaned out all the pond's spatterdocks for food. I want to preserve those as the pond is very short on shore plants for forage fish shelter. It destroys other pond plants I try to establish. I have no clue where it goes or what it is eating to survive. They can live 8-15 years. Their offspring next spring?
Get rid of them as safely & quickly as you can! Local trapper best answer!
They may move on once they run out of food on the island, but I wouldn’t rely on that happening soon. Beavers will travel a fair distance from the water for suitable trees, and 75 yards isn’t much of a barrier for them. If they still have access to the trees across the road, they may simply start using those instead. If they aren’t causing problems with your dam or shoreline, I’d keep an eye on them for now and see whether their activity decreases once the island is stripped of the remaining trees. A trail camera would be useful for figuring out whether they’re still regularly coming back.