BTW, as for the "rogue" theory, beavers naturally expand their territory as the population increases and food sources decrease. Yup, even if you relocate or kill them, you'll have the same problem recurring.

To kill them is a shame, so, all you can do is relocate them... just make sure you do it as soon as they begin a dam because the energy they spend is in direct proportion to their winter survival rate. Like I said above, there comes a point when they would be better off being shot than starving to death over the winter. (Are you in a cold winter zone?)