I spend a couple of hours soldering up all the required displays. I now have 10 displays each made out of a pair of 2-digit displays that I found in a bag I bought from Electronic Goldmine about 15 years ago.
I epoxied the displays together in pairs and then sat them up on my desk on a long line so I could easily wire them up with 0.2mm insulated wire point-to-point style. The insulation on the wire is quite easily solderable using a soldering iron set to 400C instead of my usual 290C. After the soldering I just cut the wires between the modules as required.
The shift registers and the resistors was just tacked onto the displays in dead bug style. Really ugly but it got the job done.
The 4-digit modules are driven by a HC595 shift register with 82 ohm resistors connected to the cathodes. So each module have 4 Anodes, VCC/GND and DataIn/Clock/Latch/DataOut that needs to be hooked to to the other modules.
The GND wire is a bit thicker that the rest of the wiring since it needs to carry quite a lot of current in total.