Jay and Raul, Thanks for your comments. Depth-of-field in with super-telephoto lenses is measured in tiny fractions of an inch. Increases in d-o-f that come with going to higher ISOs and smaller apertures are also tiny and are often barely noticeable. In addition, the smaller apertures result in slower shutter speeds which result in more images lost to subject movement.
In light of the above I have--for the past 28 years--been largely working at the wide open aperture, focusing on the bird's eye, and letting the d-o-f fall where it may
. As I have been doing sort of OK I will not be changing gears anytime soon. Do know that there are a very few noted bird photographers who for the most part work at smaller apertures than I do (but most of them work more with small songbirds.... When working at point blank distance a bit of extra d-o-f can help and is possible if the bird remains still for an instant at the moment of exposure.