Totally broken fullscreen when mirroring a subset of the monitors

I have two monitors (in the logs: DP-2, DP-4) and one beamer (HDMI-0) connected to this computer via a GTX 970.

Since this computer is used as a presentation device, I want to configure the beamer output to mirror one of the two monitors, so that the presenter can see what's being projected and keep a spare screen for notes or other stuff.

(As an unrelated note, the @$%#~£ builtin applet in System Settings *obviously* does not make this setup possible out of the box, but only let me mirror *all monitors* or arrange them side by side. One needs to resort to xrandr / nvidia-settings / editing ~/.config/monitors.xml to make this work; preferably the last one, as it's the only way to make these settings permanent.)

In the end, this is the setup I want:

$ xrandr

Screen 0: minimum 8 x 8, current 3840 x 1080, maximum 16384 x 16384
DVI-I-0 disconnected (normal left inverted right x axis y axis)
DVI-I-1 disconnected (normal left inverted right x axis y axis)
HDMI-0 connected primary 1920x1080+1920+0 (normal left inverted right x axis y axis) 0mm x 0mm
   1920x1080 60.00*+ 59.94 50.00 29.97 23.97 60.00 50.04
   1600x1200 60.00
   1440x900 59.89
   1400x1050 59.98
   1366x768 59.79
   1280x1024 75.02 60.02
   1280x800 59.81
   1280x720 120.00 60.00 59.94 50.00
   1024x768 119.99 75.03 70.07 60.00
   800x600 75.00 72.19 60.32 56.25
   720x576 50.00 50.08
   720x480 59.94 60.05
   640x480 75.00 72.81 59.94 59.93
DP-0 disconnected (normal left inverted right x axis y axis)
DP-1 disconnected (normal left inverted right x axis y axis)
DP-2 connected 1920x1080+1920+0 (normal left inverted right x axis y axis) 527mm x 296mm
   1920x1080 60.00*+ 59.94 50.00 60.05 60.00 50.04
   1600x1200 60.00
   1600x900 60.00
   1280x1024 75.02 60.02
   1280x720 60.00 59.94 50.00
   1152x864 75.00
   1024x768 75.03 60.00
   800x600 75.00 60.32
   720x576 50.00 50.08
   720x480 59.94 60.05
   640x480 75.00 59.94 59.93
DP-3 disconnected (normal left inverted right x axis y axis)
DP-4 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 527mm x 296mm
   1920x1080 60.00*+ 59.94 50.00 60.05 60.00 50.04
   1600x1200 60.00
   1600x900 60.00
   1280x1024 75.02 60.02
   1280x720 60.00 59.94 50.00
   1152x864 75.00
   1024x768 75.03 60.00
   800x600 75.00 60.32
   720x576 50.00 50.08
   720x480 59.94 60.05
   640x480 75.00 59.94 59.93
DP-5 disconnected (normal left inverted right x axis y axis)

DP-4 on the left, DP-2 on the right, HDMI-1 mirroring DP-2.

When I configure the system this way, windows don't properly enter fullscreen any more.

The launcher bar and the menu bar are still visible, even visually covering parts of the window. The window just becomes frameless and somehow maximized.

Cf. the attachment, in which this very Firefox window is not-so-fullscreen. This is reproducible with any standard Ubuntu app: Firefox, a terminal, LibreOffice, ...

For extra levels of brokeness:

1) when using Firefox, the launcher and the menu bar do not actually react to any mouse event. Clicks on top of them get delivered to the underlying window.

2) any "popup" opened by the fullscreen window actually makes the launcher and the menu bar disappear. This includes tooltips, contextual menus, the "burger menu" in Firefox and so on.

Fullscreen works properly only when either *all* the monitors are mirroring each other, or they're not overlapping (all side by side or similar), i.e. the only configurations that are available from the @$%#~£ builtin applet).

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: unity 7.4.0+16.04.20160526.1-0ubuntu1
ProcVersionSignature: Ubuntu 4.4.0-28.47-generic 4.4.13
Uname: Linux 4.4.0-28-generic x86_64
NonfreeKernelModules: nvidia_uvm nvidia_modeset nvidia
.proc.driver.nvidia.gpus.0000.01.00.0: Error: [Errno 21] Is a directory: '/proc/driver/nvidia/gpus/0000:01:00.0'
.proc.driver.nvidia.registry: Binary: ""
.proc.driver.nvidia.version:
 NVRM version: NVIDIA UNIX x86_64 Kernel Module 361.42 Tue Mar 22 18:10:58 PDT 2016
 GCC version: gcc version 5.4.0 20160609 (Ubuntu 5.4.0-6ubuntu1~16.04.1)
.proc.driver.nvidia.warnings.fbdev:
 Your system is not currently configured to drive a VGA console
 on the primary VGA device. The NVIDIA Linux graphics driver
 requires the use of a text-mode VGA console. Use of other console
 drivers including, but not limited to, vesafb, may result in
 corruption and stability problems, and is not supported.
.tmp.unity_support_test.0:

ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
BootLog:

CompizPlugins: No value set for `/apps/compiz-1/general/screen0/options/active_plugins'
CompositorRunning: compiz
CompositorUnredirectDriverBlacklist: '(nouveau|Intel).*Mesa 8.0'
CompositorUnredirectFSW: true
CurrentDesktop: Unity
Date: Wed Jul 13 13:57:37 2016
DistUpgraded: Fresh install
DistroCodename: xenial
DistroVariant: ubuntu
DkmsStatus:
 bbswitch, 0.8, 4.4.0-28-generic, x86_64: installed
 nvidia-361, 361.42, 4.4.0-28-generic, x86_64: installed
GraphicsCard:
 NVIDIA Corporation GM204 [GeForce GTX 970] [10de:13c2] (rev a1) (prog-if 00 [VGA controller])
   Subsystem: eVga.com. Corp. GM204 [GeForce GTX 970] [3842:4975]
InstallationDate: Installed on 2016-07-13 (0 days ago)
InstallationMedia: Ubuntu 16.04 LTS "Xenial Xerus" - Release amd64 (20160420.1)
MachineType: ASUS All Series
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-4.4.0-28-generic.efi.signed root=UUID=e10d71a4-3fe8-4cc0-b793-a3f68889193d ro quiet splash vt.handoff=7
SourcePackage: unity
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 08/08/2014
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: 2105
dmi.board.asset.tag: To be filled by O.E.M.
dmi.board.name: B85M-E
dmi.board.vendor: ASUSTeK COMPUTER INC.
dmi.board.version: Rev X.0x
dmi.chassis.asset.tag: Asset-1234567890
dmi.chassis.type: 3
dmi.chassis.vendor: Chassis Manufacture
dmi.chassis.version: Chassis Version
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvr2105:bd08/08/2014:svnASUS:pnAllSeries:pvrSystemVersion:rvnASUSTeKCOMPUTERINC.:rnB85M-E:rvrRevX.0x:cvnChassisManufacture:ct3:cvrChassisVersion:
dmi.product.name: All Series
dmi.product.version: System Version
dmi.sys.vendor: ASUS
version.compiz: compiz 1:0.9.12.2+16.04.20160526-0ubuntu1
version.ia32-libs: ia32-libs N/A
version.libdrm2: libdrm2 2.4.67-1ubuntu0.16.04.1
version.libgl1-mesa-dri: libgl1-mesa-dri 11.2.0-1ubuntu2
version.libgl1-mesa-dri-experimental: libgl1-mesa-dri-experimental N/A
version.libgl1-mesa-glx: libgl1-mesa-glx 11.2.0-1ubuntu2
version.nvidia-graphics-drivers: nvidia-graphics-drivers-* N/A
version.xserver-xorg-core: xserver-xorg-core 2:1.18.3-1ubuntu2.2
version.xserver-xorg-input-evdev: xserver-xorg-input-evdev 1:2.10.1-1ubuntu2
version.xserver-xorg-video-ati: xserver-xorg-video-ati 1:7.7.0-1
version.xserver-xorg-video-intel: xserver-xorg-video-intel 2:2.99.917+git20160325-1ubuntu1
version.xserver-xorg-video-nouveau: xserver-xorg-video-nouveau 1:1.0.12-1build2
xserver.bootTime: Wed Jul 13 13:42:05 2016
xserver.configfile: default
xserver.errors:

xserver.logfile: /var/log/Xorg.0.log
xserver.outputs:

xserver.version: 2:1.18.3-1ubuntu2.2