1/focal length is for hand-held shots. 900mm is a fair amount of zoom and it would leave the camera more susceptible to any movement, but a tripod (and to a lesser extent a monopod) removes most of the concern about camera movement. If you're using a tripod and it isn't windy and you're using a cable release or a remote or the camera's delay, the only factor you need to worry about is movement within the scene that you're shooting. I mentioned wind because even on a tripod, gusts of wind can move a camera. A monopod will pretty much remove the risk of camera shake, but you're still left with the need to hold the camera steady for slow shutter speeds. Long exposure shots still require a tripod or a secure resting place for the camera.

You actually have quite a good camera, but you're not getting the best out of it. As twr suggested, in the scenes as shown, 1/60 would probably have been fast enough. The only thing that might have necessitated a faster shutter speed is foreground vegetation swaying in the wind, but in these shots there isn't any. Wind-blown fur can be a problem, but these guys have short, wiry fur, so not much of a problem there, and they're not prone to quick, unexpected movements either (just don't forget that they can run surprisingly quickly - faster than you ).

Rongnongno's suggestions for PP sound very masterful, but if you're not at that level yourself, or if you're looking for something a bit simpler and more straight-forward, making the right adjustments to Contrast, Clarity, Blacks, Shadows, Brightness, Highlights and Whites (with possible tweaks to WB, Saturation, Vibrance and colour in the HSL section) would be enough to lift the shots to another level. Soft light can provide many advantages for shooting, but one thing it won't do is give you contrasty images. Your first shot in particular is in need of some more contrast/clarity - just watch out for the blacks, and to a lesser extent the shadows, becoming too dark and heavy. It's perfectly legitimate to use the Blacks slider to adjust the general level of brightness at the dark end of the luminosity scale. However, if you do use it to lift the dark end you might find that you need more contrast to counteract the resulting flatness (it's a balancing act, but it can yield good results if you do it properly).

Not forgetting that raw files should always get some kind of sharpening and denoise. Whenever there's a lot of ISO noise I always make my sharpening edge-oriented to avoid aggravating the graininess, and if there are specific areas that would benefit from general sharpening (e.g. fur), you can apply it to those areas with the Adjustments brush (or whatever your editor's equivalent is). The same thing applies to any areas that might benefit from extra denoise, for example to reduce the ISO graininess. I often use extra denoise to soften backgrounds. If you have Lightroom you'll find that images taken at high ISOs usually benefit from some Colour Denoise to clean them up a bit.

I often have to use ISO 3200 on wildlife because they tend to be out in weak light. Also with wildlife you need to meter on the critter and Bison are very dark.

The OS on the Sigma 150-600 is likely good. It is pretty good on my older 150-500. But even with my Nikon 200-500, which has awesome VR and fixed max aperture of 5.6 I have found that to get sharpest pics handheld It works best if I keep the shutter speed up to 1/500. In this case ISO 1600 and 1/500 would have likely yielded sharper images.

I now mostly use M mode and auto ISO on wildlife (handheld) with my Nikon 200-500, with the f-stop set to 5.6 and the min shutter speed set to 1/500. Spot or center weighted metering. I usually use it on my D5300 for the crop factor but use the same settings when I use it on my D800. ISOs range from 200 to 6400.

Which Nikon? I have the same lens and never have to use 3200 iso ... even shooting football in crappy high school stadium lighting. The only reason to shoot at 1/1000th sec. is to stop action ... cutting the speed down to say 200 should give you a lot of leeway. These are basically cattle standing still ... limited movement ... a high shutter speed isn't required. You could probably go as low as 1/60th ands still get good focus. That would allow you to use ... say 400 iso. Believe it or not the program mode is really good at giving you basic settings .. then use similar settings as a basis for manual shots.

Which Nikon? I have the same lens and never have to use 3200 iso ... even shooting football in crappy high school stadium lighting. The only reason to shoot at 1/1000th sec. is to stop action ... cutting the speed down to say 200 should give you a lot of leeway. These are basically cattle standing still ... limited movement ... a high shutter speed isn't required. You could probably go as low as 1/60th ands still get good focus. That would allow you to use ... say 400 iso. Believe it or not the program mode is really good at giving you basic settings .. then use similar settings as a basis for manual shots.