You said you already got
xrandr to display on a smaller portion of the screen, but that it’s centered. If there is any way in your monitor settings to move the displayed portion to the left edge of the screen, then you’re done.
Nesting X Servers
Try Xephyr or Xnest. They allow you to run an X server inside another X server. So something like this might work:
Xephyr -screen 1200x1080 :1
Set the resolution to whatever viewable area you have on your screen. Then you have an X server that only takes a portion of the screen.
For your first X server, you may not need to run a window manager, if you can get your
.xinitrc to start Xephyr in the right size and location on the screen.
Xephyr -geometry 800x600+0+0 doesn’t work for me though.
You’ll need to run a window manager/desktop environment inside Xephyr. I don’t know the best way to do this at the moment.
Making your window manager avoid part of the screen
This is kind of an ugly fix, but you could create a large panel with nothing in it that covers the dead part of the screen. Set the panel so that no windows can cover it. This won’t help if a program (like a video player) tries to draw on the full screen.
Question on Stack Overflow: X in a window in X