Ah yeah, I think you're right. I somehow got setgid exactly the wrong way around.
Ownership looks correct. So does the write access for the group. But there's no 's' in the Files directory. You should set it there as well: sudo chmod g+s /data/Files
In case that doesn't work, I always like to then just grant write permissions for everyone and see if that works. Maybe there's an issue hidden somewhere else.