Once I got the early 4-display test PCBs from OSH Park, the pieces started falling into place. 

I was able to buy about 380 display modules. Each display controller could handle 16x12 segments, which I could arrange into 6x4 7-segment (really 8 w/ the dot) panels. 14 of these was 336 modules, leaving me room to spare for failures. And thanks to the chip's versatile use of address pins, I could easily fit them all on to the same bus.

I put together a full 6x4 module PCB, sent it off, and almost immediately realized that I had made a crucial mistake. (Insert forehead slap emoji here.) In the process of renaming some pins I had forgotten to hook up one of the address lines! I ordered some more from Elecrow via DHL and began bodge-wiring up a few boards.

(Yes, I use autorouters. As an artist, I like the strange, synthetic appearance, and it lets me work much more quickly. I do hand-route differential pairs.)

Just as well, ordering another round of boards gave me time to get a stencil and learn how to properly paste my boards (bad examples visible below).

Here are some views of the assembly process:

Attaching the panels together turned out to be a bit of a challenge. I had in mind that I would solve the mechanical attachment stuff with some magic powder later in the process. Lesson learned, always make sure you have some kind of mounting points, even teensy... and don't half-butt your connectors.

I ended up taking pins from 0.1" header, finding the most flat surface in our condo, and laying them flat across the board-edge connector pads to connect the boards together:

(I'll grab a picture of the final connected versions next time I have it open.)

and before I knew it... first light!