Adam, please don't take my hunch as a fact - it just looks so absolutely very similar of what we got back a few years when this happened with the Leica M8 and M9.
If this would happen to me with my S2, my very first reaction when seeing such a shot on the LCD would be to repeat the shot, taking care of the positioning of the strong light source (just turn your position a fraction of an angle).
Here is something I could find about the "green stripe problem" with the M8/9 cameras:
Leica M9 Review, Tests, Comparisons
specifically this photo shows the phenomenon, caused by a strong light source hitting the edge of the sensor in just the right angle to overload the photocells in the sensor half next to the light source:
You will find some technical info, written up by Mark here on LUF:
green blob summary - Leica User Forum
Nevertheless, I would reproduce the issue, save DNG files and get in touch with a technical specialist of the S cameras in WETZLAR/ Germany.
I am sure this is the very best source of getting a confirmation whether this is behavior to be expected or indeed a camera defect related issue.
Good Leica NJ supplied a new camera (the most important for you to keep working). I am a bit surprised though by the lack of detailed information, helping you to be assured of the cause of the issue.
Good luck, and above all enjoy the S system - it's a great system even though you are up to a rocky start.