After screwing with the laser projector for a while, I got it to work a little better, mostly by using a bit of fishing line glued to the mirrors to pull them in one direction. Each had a specific direction it had to be pulled in, and so I think this helped because of the weak -12 volts provided by my power supply, and pulling the mirror in one direction means that it relies mostly on the stronger +12 volt supply.
Anyway, this is what it looks like now:
The lines aren't exactly straight, as made obvious by the square, but unlike before, the errors it makes now are repeated identically for each frame, and so at least the image is stable.
On the web site I linked to before, I found a few of that person's pictures included with his image editor, and so I tried them out on my projector. My projector is way too slow for such complex images, but that didn't stop me from using a 15 second shutter time to make visible something that is being drawn so slowly that it is otherwise unrecognizable. There are some stray lines included since my system doesn't have the ability to turn off the laser.
I've been planning to use DC motors the next time I build a CNC mill, and I've had people tell me that I have to use stepper motors because DC motors won't be capable of fine positioning. Well, at a distance of 12 inches, the projected image is only 1 inch wide, which means I'm drawing these things with only 5 degrees of movement. I only need positioning accurate to within 36 degrees for my CNC mill, whereas it seems I'm getting far better than 1 degree positioning with this laser projector.