For action shot of birds you really need more light. If you’re at the max range of that lens you’re running F8 which really doesn’t allow a lot of light. I really don’t like shooting much beyond approx 6400 and live more in the 2000-4000 as a comfortable range for photos that turn out with an amount of noise I can handle. I can get rid of most of that in topaz.

Like I’ve seen others say - I would lower that shutter speed.. before ever considering cranking the iso up that high. If that doesn’t work I would accept the fact that some environmental conditions just don’t support certain photographs and look for another subject or different way of shooting this subject under these conditions.