I Would love to adjust, especially saturation, in the shadows separately. Hue VS Sat can also be helpful. Sometimes there is too much color in the shadows, but the rest of the tones and color in the image is great.
You mentioned Hue vs. Sat, which I've seen in video color grading programs. I'd love to see some of the things I see in these programs come to Photoshop, especially the very helpful color scopes, but I fear it will be a while before we see major changes or additions to Photoshop's primary tools. In the mean time, you may want to familiarize yourself with Blend If, located in a layer's Blending Options. You can do exactly the thing you describe. It's especially powerful when working in Lab, but that might not be for everyone.
That is exactly how I do use it with layer adjustments. I just wish it was in lightroom. The only way to work around it within lightroom I found is to fiddle with the saturation and vibrance balance. Only works to an extent. It would be so powerful if lightroom could split the HSL to affect, shadows midtones or highlight independently, like shadow hsl, midtone hsl and highlight hsl sliders. :)