That is what the 600mm f/4.0 is for
The listing is really good on those. I am struggling with my BIF shots because even on a sunny day with blue sky the sky sky tends to get blown when exposing the dark feathers, or I expose for the sky and get no details in the bird. A CPL helps but I can't afford to loose 2 stops when I am already at f/8 and trying to maintain at least 1/500th .
Shooting at sunrise and sunset with the sun behind you helps a bunch but often that isn't possible.