So a bit far from you, but river Tay is sadly washed full of the rodents.
The laird at Meikleour's been spending millions to put cages on the majority of the riverbank to protect his farms - stopped the beavers tunneling through to the fields, and looks pretty... NOT...
Another beat I fish at on the lower river (Upper Redgorton) has a wee burn that comes into the main river on the beat. It historically is a very significant spawning burn on the lower river for the salmon. We're not quite sure how well they're going to spawn now, as the beavers are felling trees left right and centre along it along with their other antics, which we suspect will be impeding spawning activities there.
Edit: To add, I did speak to the head ghillie at Meikleour last year just to ask about the control measures that are available, and yes, because they have farmland (at the appropriate grading) they would be allowed to shoot them, but I believe the licence is such that you can only shoot them in the Autumn/Winter and after dark? Which is not a massively appealling prospect for the estate.