I've made a tutorial how to achieve this effect in Premiere Pro CC using Lumetri Color:
Yes, this is possible to desaturate the darkest shadows with Premiere Pro CC using Lumetri Color. Please check out my tutorial steps here:
Stray Angel had a tip that is very useful not mentioned here, gel the lights illuminating the greenscreen with a green gel, it makes the green screen really vibrant and key-able.
Here's another test I ran showing the unbelievably bad noise performance in ISO 10k, but considerably cleaner image at ISO 12.8k.https://vimeo.com/160340989
Here's the place to complain to Sony about the issue:http://community.sony.com/t5/Join-the-Inspiration/Please-Fix-a7sII-Slog-...
Here's another test looking at the noise issue, most specifically how dialing up to 10k ISO is much noisier than dialing down from 12.8k IS0.
This is very odd noise performance issue and might point to a firmware issue specifically with shooting S-Log3.