Before you sacrifice ISO to increase DOF, be realistic in terms of expectations. With small distant moving subjects, AF is challenging takes practice. Even with the newer AF system of the D4/D800, and a larger subject, 65% success is reasonable.
I've recently used the 300 f/4 and D800E for photos of gulls and pelagic birds on the ocean. AF success is remarkably low even and the misses are large enough that a stop or two more in DOF won't matter.
Do keep the shutter speed high - 1/1000 sec or more. I'd suggest an aperture slightly stopped down - but not beyond f/5.6. Use the center AF sensor only. Try to track and follow the subject if its flying. Otherwise consider other tools and techniques to increase stability.