Beautiful picture!! Shame that there just wasn't a better place to be, but sometimes there's just nothing you can do. Except in post... :roll:
I know this is small, but I hope maybe it will be helpful!
I cropped so that you'd be closer to the eagle. Then I used a "paint with light" technique.
1. I created a new layer, filled it with 50% gray, & set the blending mode to "soft light".
2. Next I used the elliptical marquee tool with a feather of 10 pixels (may have to change value with a full res photo) to select an oval area around the eagle.
3. CTRL-I to invert the selection.
4. Select a large, soft paintbrush & paint black on the 50% gray layer. You will be adding shadow to the area outside the oval.