As mentioned in #47, same problem on trusty + xenial HWE stack (14.04.5).

Additionally, had a gcc version mismatch, don't know where that came from.

Meta package gcc was 4:4.8.2-1ubuntu6, but /usr/bin/gcc (and corresponding package gcc-4.8) was 4.8.5-1ubuntu1~14.04 .
I also had installed just gcc-4.9-base (without even gcc-4.9) due to some dependencies.

Went back to -112 kernel.

Tried #57 (@cjjefcoat) steps, but did not trigger a driver rebuild.

I had a lot of PPA-s and manual file-wrapped deb lines in /etc/apt/sources.list.d/.
I had ubuntu-toolchain-r/ppa, not ubuntu-toolchain-r/test, but IIRC purging failed somehow (cant remember, couple of days ago), probably due to same mismatch.

So just deleted all entries from /etc/apt/sources.list.d/, manually cleaned /etc/apt/sources.list, updated repo cache.

Then tried to force-install (downgrade) gcc-4.8 and gcc-4.8-base to 4.8.4-2ubuntu1~14.04.4, to make it in sync with the gcc package again.
After force-picking all the needed dependencies, I ended up with
sudo apt-get install gcc-4.8 gcc-4.8-base:i386=4.8.4-2ubuntu1~14.04.4 gcc-4.8-base:amd64=4.8.4-2ubuntu1~14.04.4 g++-4.8=4.8.4-2ubuntu1~14.04.4 libstdc++-4.8-dev=4.8.4-2ubuntu1~14.04.4 libgcc-4.8-dev=4.8.4-2ubuntu1~14.04.4 cpp-4.8=4.8.4-2ubuntu1~14.04.4 libgl1-mesa-dri libgfortran3=4.8.4-2ubuntu1~14.04.4 libstdc++6=4.8.4-2ubuntu1~14.04.4 libquadmath0=4.8.4-2ubuntu1~14.04.4 libgomp1=4.8.4-2ubuntu1~14.04.4 libitm1=4.8.4-2ubuntu1~14.04.4 libatomic1=4.8.4-2ubuntu1~14.04.4 libasan0=4.8.4-2ubuntu1~14.04.4 libtsan0=4.8.4-2ubuntu1~14.04.4

Somewhere in the process (do not remember when) the nvidia driver, dkms, the HWE stack (kernel + xorg) and some other stuff got uninstalled (due to missing dependencies).
Probably I could have avoided that and was just too strict on removing potentially screwed up stuff.
I think I totally removed gcc-4.8 or even all of gcc before reinstalling with the (assumed) correct version.

So after "aligning" gcc, I installed back the xenial kernel (a'la ubuntu wiki HWE page, for multiarch):
sudo apt-get install --install-recommends linux-generic-lts-xenial xserver-xorg-core-lts-xenial xserver-xorg-lts-xenial xserver-xorg-video-all-lts-xenial xserver-xorg-input-all-lts-xenial libwayland-egl1-mesa-lts-xenial libgl1-mesa-glx-lts-xenial libgl1-mesa-glx-lts-xenial:i386 libglapi-mesa-lts-xenial:i386

There the amd64 and i386 versions of libgl1-mesa-dri-lts-xenial had a /etc/drirc conflict.
Apt was useless, just returned a dpkg fail (with or without -f).
Overwriting /etc/drirc with /etc/drirc.dpkg-new was not enough, had to remove /etc/drirc alltogether.
THEN on `sudo apt-get install -f` apt asked me to resolve /etc/drirc conflict using apt-s command line query.
One said Unigine Heaven 3.0 this and that setting, the other said "Unigine Heaven 3.0 and older contain too many bugs and can't be supported [...]".
Went with the second, seemingly newer one.

Then came the nvidia driver (with forcing the dependencies previously removed by apt):
sudo apt-get -f install nvidia-340 dkms acpid lib32gcc1 libc6-i386 nvidia-prime nvidia-opencl-icd-340

This compiled the driver and
modinfo nvidia-340 -k 4.4.0-116-generic | grep vermagic
said retpoline.

Reboot, works.

Just like that. :)

I guess the system is ripe for reinstall. :)