Good points.Based on the metadata and your comments:
- FASTER shutter speed, let the ISO go up to give you the shutter speed you need to use. Better to have a noisy sharp image, than a noise-free blury image.
- With the D3400m you are shooting an APS-C camera, so at 500mm, you are shooting at 15x magnification. I would definitely shoot with VR on. Even with VR, I would try to shoot at 1/1000 sec, and if I feel unstable (like being blown by the wind), I would crank it up faster.
With the FF/FX Z7, the lens magnification drops down to 10x. I would still shoot at 1/1000, even with IBIS. I want the odds in my favor.
- VR. I don't know how the Z7 handles dual IS, IBIS + VR. But, in general, I take ALL the technical help that I can get, especially with a LONG lens. So if the Z7 can work IBIS + VR, I would do that.
- I don't know which AF mode you are using, but I would use a FIXED AF point, so that I can select exactly what I want the camera to focus on. Example, the camera could select to focus on the brush between you and the animals. My experience with zone/area focus has been, that about half the time, the camera will focus on something other than MY subject. So, except in rare instances, I want to select what to focus on, not the camera.
- Try to be precise about what you focus on.
- As was mentioned the rear cat seems to be what was focused on, not the more visible front cat.
- The pack of wolves is a problem. There is significant front to back depth, which the lens at f/5.6 does not have enough DoF to handle. So you have to select which wolf you want in focus and let the rest go OOF, or decrease the aperture, to get more DoF. In the case of a group of animals, you may want to shift from f/5.6 to f/11, to get more DoF, at the cost of higher ISO.
- If you are cropping deep into the image, it may be hard to precisely position the AF point when you shoot. But try. As @gchappel said, practice, you WILL get better.
- IBIS and VR will compensate for your movement, not the subject's movement, so for wildlife, I would not drop the shutter speed much. Although in these cases at 1/800 sec, I don't think subject movement is an issue.
- With the Z7, you can preview the exposure in the EVF, so take advantage of that.
- Don't underexpose the subject in the shade. You many have to let the bright snow blow out. Recovery of underexposed images results in noise/grain, and lack of contrast. Learning to use the EVF takes a bit of practice.
- If you can set the EVF to display highlights, you can see what will blow out. That makes it easier to see how much you can push the exposure, and when you have to back off.
On the Z7, you can't set the EVF to display highlights. You only have the live histogram.
Steve Perry on long lens technique (using a tripod) here
Steve Perry on sharpness techniques here