Frank, unfortunately I can't help with raw editing. However, it looks like the D500 focus system tracks very skillfully (I think Ilkka has posted about this recently, too). It appears to hold focus on the bird across a quick succession of bright and dark backgrounds and even into the tree for all but the last 2 or 3 frames. In similar situations I find the D810 often has trouble initially grabbing focus on dark birds against a bright sky (more reliable with seagulls on a dark background). The D810 focus system also seems to be easily distracted by detail in the background, so will often drop focus if the bird passes in front of a tree. Your sequence suggests that the D500 improves performance on both counts.
For the record, my comments apply to the AF-C / D9 focus mode which I use most commonly. Also not a complaint about the D810. Rapid-fire autofocus still seems like magic to me, and the D810 is a truly outstanding camera for my purposes in many other ways as well.
