There are now more reports of the same issue on other people's machines. I do not believe this is simply a misconfiguration on my part, and this issue still needs to be addressed.
I did, however find the answer to almost make this work for me at https://answers.launchpad.net/ubuntu/+question/67975 . I say almost, though, because the right side of my desktop background is now messed up. I will try to attach a scaled-down screenshot.
(Again,) This still needs to be fixed so the average dude can enjoy effects GNU/Linux properly working.
Integrated video hardware in Asus M2A-VM with (according to manual) ATI Radeon X1250-based graphics
Both DVI-D and RGB are in use for dual-monitor set-up
256 MB shared vram
The driver is radeon.