I try to follow the "rules" especially rule of thirds as I find it creates a more pleasing photo. But I am perfectly happy to break rules - sometimes it works for the particular image and sometimes, it is all one can achieve especially when shooting fast moving animals or birds. I also prefer to give my subjects more room in front to move into but if I don't have time to compose that way, I am comfortable so long as there is some room in front of the subject. My preference is to shoot at f/5.6 or larger apertures to create an out-of-focus background but again, for fast moving birds or animals I will use f/8 or f/11 to ensure the subject stays in focus. The photos, of the Frogmouth and Chimango Caracara, are all examples of nicely blurred backgrounds. The Tui illustrates a common background when shooting birds - featureless blue sky and also is an example of shooting upward in lieu of at eye level - fairly common as birds roost in high places.

Regarding crafting great bird photos in general. Making camera adjustments  such as exposure compensation, ISO, aperture or shutter speed.

Please elaborate a little regarding the possibility of missing a shot while making a camera adjustment (one possibility would be to have two cameras available)and the possibility to make adjustments post production using editing software.