Shutter speed should be as fast as possible for D800/E. Recently someone suggested that it should be 3x the normal 1/focal length. For example 1/1200 for 400mm, and for birds should be 1/1200 x 3 or 1/4000.
Another thought - what about Auto ISO with max ISO of 6400?
I haven't tried this on my D800 but will do it soon.