It took a little bit of work, but I finally got a video of the driver in action. It's low quality, and the burn wasn't as clean as the one I did before I started recording, and I managed to burn my fingers at the end of the filming, but at least I managed to get it going.
You'll notice that the oscilloscope in the background keeps displaying a sawtooth wave whenever the electrodes are making contact. The rising parts of the wave are the charging pattern from the bench power supply (for safety reasons, I couldn't run the unit from wall current while it was hooked to the oscilloscope), and the falling periods are the discharge from the capacitors to the workpiece.
I also have a few pictures of the equipment to show you:
*The power supply board, freshly soldered and ready to go
The logic board and capacitors, on a solderless breadboard.
The soda can I plasma-cut before attempting a video -- it took three seconds to make that hole!. Apparently this circuit is camera shy.
The soda can I cut in the video. I realized after I finished the video that I didn't properly sand away the insulative enamel on the outside of the can, so that's probably why it took me so long to strike a proper arc and cut all the way through.