Ubuntu – Login Loop – “BadValue (integer parameter out of range for operation)” – 16.04

I was running Ubuntu 16.04 LTS with a manually installed NVIDIA 361 driver. After upgrading the driver to v367 I am now locked out of Unity with a login loop with the following error in .xsession-errors:

X Error of failed request:  BadValue (integer parameter out of range for operation)
  Major opcode of failed request:  154 (GLX)
  Minor opcode of failed request:  3 (X_GLXCreateContext)
  Value in failed request:  0x0
  Serial number of failed request:  32
  Current serial number in output stream:  33
openConnection: connect: No such file or directory
cannot connect to brltty at :0

I also found this in the Xorg logs:

[ 2312.921302] NVRM: Your system is not currently configured to drive a VGA console
[ 2312.921304] NVRM: on the primary VGA device. The NVIDIA Linux graphics driver
[ 2312.921305] NVRM: requires the use of a text-mode VGA console. Use of other console
[ 2312.921305] NVRM: drivers including, but not limited to, vesafb, may result in
           NVRM: make sure that this kernel module and all NVIDIA driver

And then this further down:

[  2850.609] (II) NOUVEAU driver Date:   Tue Dec 8 15:52:25 2015 +1000
[  2850.609] (II) NOUVEAU driver for NVIDIA chipset families :
[  2850.706] (EE) [drm] Failed to open DRM device for (null): -22
[  2850.706] (EE) [drm] Failed to open DRM device for (null): -22
[  2850.706] (EE) [drm] Failed to open DRM device for pci:0000:02:00.0: -22
[  2850.706] (EE) No devices detected.
[  2850.706] (II) Applying OutputClass "nvidia" to /dev/dri/card0
[  2850.706]    loading driver: nvidia
[  2850.706] (==) Matched nvidia as autoconfigured driver 0
[  2850.706] (==) Matched nvidia as autoconfigured driver 1
[  2850.706] (==) Matched nouveau as autoconfigured driver 2
[  2850.706] (==) Matched nvidia as autoconfigured driver 3
[  2850.706] (==) Matched nouveau as autoconfigured driver 4
[  2850.706] (==) Matched vesa as autoconfigured driver 7
[  2850.706] (II) LoadModule: "nvidia"
[  2850.706] (II) Loading /usr/lib/xorg/modules/drivers/nvidia_drv.so
[  2850.708] (II) Module nvidia: vendor="NVIDIA Corporation"
[  2850.708] (II) LoadModule: "nouveau"
[  2850.708] (II) Loading /usr/lib/xorg/modules/drivers/nouveau_drv.so
[  2850.708] (II) Module nouveau: vendor="X.Org Foundation"
[  2850.708] (II) UnloadModule: "nouveau"
[  2850.708] (II) Unloading nouveau
[  2850.708] (II) Failed to load module "nouveau" (already loaded, 21886)
[  2850.709] (II) LoadModule: "vesa"
[  2850.709] (II) Loading /usr/lib/xorg/modules/drivers/vesa_drv.so
[  2850.709] (II) Module vesa: vendor="X.Org Foundation"
[  2850.709] (II) NOUVEAU driver Date:   Tue Dec 8 15:52:25 2015 +1000
[  2850.709] (II) NOUVEAU driver for NVIDIA chipset families :
[  2850.709] (II) NVIDIA dlloader X Driver  364.19  Tue Apr 19 13:48:55 PDT 2016
[  2850.709] (II) NVIDIA Unified Driver for all Supported NVIDIA GPUs
[  2850.709] (II) VESA: driver for VESA chipsets: vesa
[  2850.709] (WW) xf86OpenConsole: setpgid failed: Operation not permitted
[  2850.709] (WW) xf86OpenConsole: setsid failed: Operation not permitted
[  2850.709] (EE) [drm] Failed to open DRM device for (null): -22
[  2850.709] (EE) [drm] Failed to open DRM device for (null): -22
[  2850.709] (EE) [drm] Failed to open DRM device for (null): -22
[  2850.709] (EE) [drm] Failed to open DRM device for pci:0000:02:00.0: -22
[  2850.709] (EE) [drm] Failed to open DRM device for pci:0000:02:00.0: -22

A web search of this error message does not yield many relevant results.

I have tried downgrading to v364 and then back to v361 to no avail
I have tried purging xserver-xorg, xserver-xorg-core, nvidia*, lightdm to no avail
I have tried reinstalling ubuntu-desktop to no avail

A complete reformat and reinstall would be hugely disruptive and I want to avoid that at all costs.

The error message in .xsession-errors always remains the same. How can I purge / restore / reset my settings and/or packages and/or libraries to a sane state without completely reformatting and reinstalling?