If beaver are in the mix, I'd make sure that whatever screen I use would be easily tipped up and cleaned when packed solid with stuff. They can move some amazing stuff (and a bunch of it too) overnight!!
You've got that right! The greatest handiwork was a 15' by 4' deep cut I made in one dam further upstream that had serious flow at the time and 2 days later they had repaired it much to my dismay at the incredible number of youg trees lost to their efforts. I do not like beavers.