I had planned to use four transistors, with resistors and diodes, to control the four annunciator lights. But Don Goris suggested that the ULQ-200X Darlington arrays would be a better choice. I did some research, and learned that this approach would yield a simpler architecture, with less soldering required. I ordered a ULQ-2004A, and it arrived two days ago.
The ULQ-2004A replaces all the transistors, resistors and diodes from the original schematic. The BusBoard-3U-CONN circuit board I will use has a very convenient layout, so that soldering in the ULQ-2004A makes all the connections from it to the DB-25 connector. I will just have to solder in the jumpers that connect the four annunciators to their power lines. And I need to trim the board down to size before I start. I will only need a tiny corner of the original board.
Yesterday I read the spec sheet again to confirm my understanding of how to hook this up, then I put it in a solderless breadboard, got out my patch leads and hooked it up to some batteries and my four annunciators. It worked! The 12V control signals caused the ULQ-2004A to control the ground path from the annunciators, allowing me to run them from 28V. And, pin 9 acts as a test switch - it I connect pin 9 to ground, all four annunciators light.
Now I need to figure out whether I should fabricate an enclosure, or whether it is OK to simply have the circuit board sitting exposed. It will probably eventually get some dust on it if it sits enclosed, but I don't know whether that is a problem or not. If I need an enclosure, I have no idea yet how to make one.