I rather like the dark background as IMO it lets the bird pop. If it was in a flower bed then the flashes could be angled to let it show or another flash could be used as a background light, maybe there would be enough daylight.
I amazes me that even 4000 shutter speed can only just begin to freeze their wings. It should also be noted that at these shutter speeds it's all high speed sync.
My goal is to try to catch a hummer eating a midge or whatever tiny insects they catch, that is a difficult set up.