So, did it work? See for yourself:
As you can see, my test was fairly succesful. The technique has its drawbacks, though: for instance, the touchscreen only works in the bit of screen where the white window is: touch an area around it and either your finger only casts a shadow from one led, making it impossible to locate its position, or the shadow falls out of reach of the CCD (which is shorter than the width of the screen). This can be solved by using more LEDs, perhaps positioned further away from the screen, and a larger or multiple line-CCDs.
The software itself isn't perfect either: it doesn't act as a driver, meaning it can't relay any of the touches to the underlying OS. It also sees every frame as a separate entity: if a finger moves to the other side of the screen and back in 1/50th of a second because of a detection glitch, the software won't filter that out in any way.
So, am I gonna improve on these points? I don't think so. While it's nice to play around with a multitouch touchscreen and the math around it was an interesting problem to solve, I still like my keyboard and trackball better. If someone wants to improve on my setup, they can be my guest: both the software for the PC and the firmware for the ATMega are downloadable and released under the GNU GPLv3. If you manage to make it do something interesting, as always, I'd appreciate it if you'd drop me a note.