I've finished wiring the columns. I imagine it would have been a little easier with solid core wiring, but as I don't have any at the moment, and it would take me weeks to get, I decided to go with the stranded wire I had on hand. In any case, that's what Jack Humbert sent as part of the 'wiring kit' with the plate.
I also added the brass spacers (before working on the columns), to make sure nothing got in the way. The spacers have heat-shrink tubing around them, although I haven't heated them up yet. I'm not sure it's really necessary. It's just there to prevent the spacers from coming into contact with any wires.
The next stage is to figure out how I'm going to connect to the Teensy. Ideally, I'd like to figure out a way to connect to it without soldering directly to it. That might not be possible do to the extra space necessary to make the wires removable. I think I mentioned I saw someone use right-angle header pins with dupont plugs to keep the teensy removable, although I think that would require sticking the Teensy in the middle of the keyboard.
The ideal location for the Teensy would seem to be under the spacebar, but that means I won't have a lot of room to wire to the side on the bottom. That might mean that the only way to fit the bottom plate to the top plate will be to use larger spacers, or to solder the teensy so it will fit under the spacebar. Until I figure exactly where the Teensy will be, I can't wire the connections to all the columns and rows, so now I guess I need to wait. I have a few parts on their way from China that will give me options to try out, like right-angle pin headers, etc. so until I get that stuff I guess I'm just going to sit and wait (unless I get too impatient and solder everything under the spacebar).