I usually print 13x19" at home, and I usually do spend quite a lot of time working the shadows to get them to print nicely.
Trimming most of your post because...how on Earth do you even find time to write that much? And that's coming from someone who writes too much on forums!
All I can say is that I only rarely encounter the issues you are complaining about. And I'm usually not using GND filters or a large number of HDR shots, but manually blending two frames.
For a scene requiring HDR I'm guessing that your shadow exposures are not bright enough. I'm also guessing that you are trying to shoot some scenes in one shot when you should have at least two. Your river shot with the blown out sky...I would shoot that as two frames on Canon or Nikon.
I can only guess because I've never been out shooting with you to observe what you're doing. But you talk as if every landscape you do has horrendous shadow noise. If that's happening then you need to adjust your shooting and processing.
You've built up in your mind how much better an Exmor sensor would be, how it would revolutionize your workflow. It's better, but it's not going to revolutionize your workflow or eliminate HDR/GND. That doesn't mean you shouldn't buy a D810 or a Sony A7 series if you want one. Just don't build up Exmor so high in your mind that you buy one and end up complaining on their boards.
So...when it comes to large size images...either something like a 1920x1200 size published online (which I've done a few times for 1x.com...they have a very large format presentation), or larger prints (not sure where the cutoff is, I usually print 13x19), then yes. I HONESTLY do believe that the 5D III suffers from it's shadow noise.
I print a lot at 16x20/24. My albums that I show to family and friends have sleeves for Epson 17x22 sheets so I don't have to cut rolls or trim while filling those. I don't struggle at those sizes...or even larger when I have occasion to print larger. I can literally think of two shots where I did not have a frame with sufficient shadow exposure and was bummed about the noise/tonality/detail in the deep shadows. Of the two, other people have only noticed one.