Re the photo above with the 400 f5.6 and 7D, please don't think that photos taken with this setup are reflective of that picture, which is a very poor shot.
I'm confused - I'll be grateful if you'll explain why it's a poor shot as it looks great to me (I was just about to comment to that effect when I saw your post). I'm probably showing my ignorance but hey ho! if you don't ask you don't learn anything!
It's lacks sharpness, suffers from from camera shake and has been heavily cropped showing a great amount of noise, I also expect it has been brightened up to bring up detail in the shadows exaggerating noise too. The has resulted in poor image quality. It does not reflect the photos you can get with this setup at that iso. Here are a couple of photos at various iso so you see the the appearance of noise. Notice the barn owl which is shot at 3200 iso which is not that noiser than the image I commented on.
Jamie, they are truly excellent, especially considering the iso. Here is a crop to emphasize what you wrote about the noise etc. All the fine structure of the plumage has been lost, so only the coarse details remain with horrendous noise. It was also taken at f/10, which spoiled what bokeh there could have been.
5D IV, 5DS R, 7D II, EOS-M, Powershot G3 X, 400mm DO II, 300/2.8 II, 1.4xTC III, 2xTC III, EF 1.8 STM, EF 70-200/4 IS, EF 24-105, 15-85, 100-400 II, Sigma 10-20, Sigma 150-600mm C, EOS-M5 15-45, f/2 22, 11-22, Samyang 8mm f/2.8 fisheye