Ordered wire came in, finished wiring LEDs in RTI dome, and (after chasing down one loose connection):

In the above test, LEDs were turned on at random; in the following test, columns were turned on sequentially starting with the top row and moving to the bottom:

Now that the wiring is done, I can post instructions for that step (and code for the test programs). The only major task left to do is putting together the control box. There are additional steps after that, but I did most of them while waiting for the wire to come in. And that'll be it for construction - the system will be ready for calibration and operation!