Can't connect third display (TV) in 12.04 beta

I have a setup with three displays:

- My primary 1920 x 1080 monitor, connected through DVI
- My secondary 1680 x 1050 monitor, connected through DVI
- My 1920 x 1080, connected through HDMI

They're connected to an AMD HD6970. Because I'm not using a DisplayPort connection it is not possible to use all three displays at the same time due to a hardware limitation. That is not a problem for me though, as I am only interested in either working (primary + secondary monitor) or watching movies / TV-shows (primary monitor + TV) and thus only need two monitors active at the same time.

After installing 12.04 last week I was able to setup my work configuration just fine. When I plug in the TV though, the OS seems to think it is a good idea to use all three monitors at the same time. As mentioned before this isn't actually possible, so everything just turns black. I can switch to a different TTY and reboot, but the only way to get an image again is to unplug at least one of the monitors. I tried copying over my old 11.10 xorg.conf from when I had just the two monitors working (with the TV connected but unused), to no avail.

I have long given up on finding a way of switching between my two setups without hours of trial and error, and I was previously content using just my work setup in Ubuntu and booting to Windows when I want to watch movies (pretty much the only thing I still use Windows for these days). As of 12.04 I'm required to crawl behind my desk and unplug the HDMI cable every time I boot back to Ubuntu, which is obviously very inconvenient.

I am using the latest proprietary drivers from the AMD website, which I installed manually (the automatic setup crashed, a different problem for which the bug reporter redirected me to an existing issue). I initially had the same problem with the open source drivers though.