HDMI output not working correctly through xrandr

You should probably simply use kscreen instead, which should solve all your issues. It will remember the settings of a previously connected screen and will restore them, once you connect it again.

If you still have such issues while still using kscreen, it should be worth a bug report.

As Kubuntu 12.04 is quite old, you probably should have a look at this.

Possible workarounds:

Use empty panels covering the damaged region to force windows using the remaining space. For example, xfce4-panel can be configured well. It depends on your desktop environment how well this works. Xfce and LXDE will work fine, Gnome will make problems, I assume. This does not help for fullscreen applications that would cover the panel, too, for example, firefox+F11, or VLC in fullscreen.

Workaround for fullscreen applications: Starting Xephyr with desired screen size, positioning it and starting applications inside it. Automate this with a script and 'xdotool`:

Xephyr :1 -screen 1500x800x24 &
xdotool search --name Xephyr windowmove 0 437

Start applications in Xephyr window with DISPLAY=:1 firefox. Xephyr does not support hardware acceleration, but virtualgl can help here.

Best workaround:

Use weston with Xwayland. It supports hardware acceleration and fullscreen applications.

Use a quite lightweight window manager like openbox at startup (or even better, one without window decorations at all like evilwm). It serves as background environment only, weston will cover it.

Create a custom myweston.ini file like this one (see man weston.ini):

[core]
shell=desktop-shell.so
idle-time=0

[shell]
panel-location=none
locking=false

[output]
name=X1
mode=1366x768

[output]
name=X2
mode=1500x768

Create a script like this one to start weston in evilwm and Xwayland in Weston (customize positions of 2 weston windows). Finally, start your desired desktop environment:

# start weston with custom config and two output windows
weston --socket=wayland-1 --config=$HOME/myweston.ini --output-count=2 >$HOME/weston.log 2>&1 &
sleep 1 # wait until weston is ready

# get window id's from logfile and move windows at target (xwininfo could give id's, too)
xdotool windowmove 0x$(printf '%x\n' $(cat $HOME/weston.log | grep 'window id' | head -n1 | rev | cut -d' ' -f1 | rev))    0 0
xdotool windowmove 0x$(printf '%x\n' $(cat $HOME/weston.log | grep 'window id' | tail -n1 | rev | cut -d' ' -f1 | rev))    1369 400

# start X server Xwayland in weston
WAYLAND_DISPLAY=wayland-1 Xwayland :1 &
sleep 1 # wait until Xwayland is ready

# start your desired desktop environment
DISPLAY=:1 startlxde

The start script above does not set up cookie authentication for X clients. Instead, you can use x11docker to have cookie authentication, too:

# start weston and Xwayland, read X environment
read Xenv < <(x11docker --weston-xwayland --gpu --output-count=2 --westonini=$HOME/myweston.ini)

# move weston windows to target locations
xdotool windowmove $(xwininfo -name "Weston Compositor - X1" | grep "Window id" | cut -d' ' -f4) 0 0
xdotool windowmove $(xwininfo -name "Weston Compositor - X2" | grep "Window id" | cut -d' ' -f4) 1367 400

# start desired desktop environment
env $Xenv startlxde

Xwayland appears as a client "window" of weston. Unfortunately, due to a bug in Weston or Xwayland, it does not always sit at position 0:0. You can move Xwayland to desired position with [META]+left-mouse-button. I wrote a bug report, but got noresponse.