I love it when things work first time. This wasn’t one of those occasions though! I had a problem where all of the output pins of the 2nd shift register were always high, meaning no digits on the display. It took some work with the voltage tester, but it was tracked down to a minute piece of stray solder, bridging two strips on the veroboard.
So the project is complete, barring the enclosure (currently the two boards are being held together by an elastic band with a piece of hard plastic in between!). So when I find a suitable sized enclosure, I’ll transfer it into there, but in the meantime, I’ll put up the board layout for the extra board, and the full code, once I add some comments.