Great tips, thanks!
robbymack: As a biologist, I know this, but thanks for making it top-of-mind. I took my new body out for the weekend and was so overwhelmed by the wealth of migratory birds that I adopted a "shoot first and ask questions later" attitude. But once I realized my abysmal keeper-rate, I knew that I should have asked a lot more questions before I even headed out to the refuge.
Regarding the light in the shot I posted, the birds were flying N-NW with the sun rising in the E-SE. I rolled out of my tent at dawn and set up my tripod in a large clearing not far from my camp, back in the forest. This allowed me an unobstructed view of the birds as they flew towards me. But this plan backfired when they spotted me, as they'd simply climb to higher altitude or veer off to avoid passing too close to a bleary-eyed photog with a shiny, aluminum tripod and long white lens.
I had much better luck (including the originally posted photo) once I retreated into the forest and shot up through a hole in the canopy. My proximity to the birds improved dramatically (shooting full-frame, 350mm), although it came at the cost of light-source-angle and fair warning.
Jeffrey: Thanks for the rules of thumb. They help a lot in establishing a baseline from which to start.
Packlight: To be clear, 1/4000 stopped things dead, but less than that resulted in blurry shots. Some of that blur was coming from inadequate focus, my movement, etc. Intuitively, I agree with what everyone has said: 1/1000-2000 should be adequate unless I'm chasing water splash, as Jeffrey pointed out. I'm not sure why my shots were begging for such a fast shutter. The shot I'm attaching to this post, for instance, is in midday sun, f/8, ISO 800, 1/3200, 150mm. But even at 1/3200 there is motion in some of the birds.
Regarding AF, Packlight, are you putting the center point on the bird, tracking the bird from center, and firing away? If so, that sounds like a good way to find and keep focus, but a potentially boring way to frame what may be a scenic background.