Great, the Ubuntu Graphics Drivers PPA is installed okay.
This may be a long shot, how about opening Additional Drivers, switch from Nouveau back to 340.98, restart, and then check if (since NVIDIA GPU becomes active) newer drivers appear?
Failing that, try installing the PPA in a live session, with either 16.04.1 or 16.10, and see if newer divers are shown. You won’t be able to restart of course, but can logout and back in.
To give you some idea of what you should be seeing, on my system (with a slightly older NVIDIA GPU), and added drivers PPA, I now see 7 different NVIDIA drivers to choose from, plus Nouveau driver.
Edit: Another idea to try. Since the graphics drivers PPA is active, possibly try…
sudo apt-get install nvidia-367- Reboot