First, download "Screen filter" from the Play store
Activate the screen filter to your liking, I recommend putting a widget on your home screen and un-tick the "enable soft-key backlight"
Now comes the extremely unscientific trick to get the soft key to be turned off, press the power key on your device to lock and unlock your device until it "forgets" to turn on the soft key back light!
I do this almost every night and usually works after 3 or 4 tries.
Maybe there is a better solution out there for the people who have not rooted their device?