After using this setup for soldering a few times, I found some minor problems with the original design.

Wood turned out to be a bad choice for the base; it soaks up solder flux and is easily burned by the iron. Also, the base is about 1/4” thick, so when trying to work on a larger PCB, or the edge of one, I had to shim it to avoid it falling off. I replaced the base with a nice thin steel plate.

My initial cut of the wood stand was a bit too short to allow for all board types, so I replaced it with a taller one. I only made it about 2” taller, but it was almost TOO tall. Using a longer bolt for the adjuster would make it so this measurement doesn't need to be so precise.

I added a little screw to the side that fixes the webcam cable in place. There's enough slack so that it can still travel the full height, but not so much that it jams things up.

At this point, I think the assembly itself is OK and it's time to look at the PC side of things. It would be nice to set this up on the bench as a standalone tool that doesn't require a computer to use. I've got a RPI and some single board Linux things sitting around, maybe I can shove one of those in a small monitor with a script to launch a webcam viewer on boot?