So far I have managed to keep the relay count pretty low, I fixed a wrong diode and all the phantom segments have disappeared. I'm wiring the rest of the segments and I realise that there is really, really a large number of diodes. This must be reduced...

And there is a pretty easy way to do it, if only I had thought about this little trick earlier. It's too late for the first proto but the PCB must certainly use it.

OK here is the trick : for example, for two consecutive digits, if there is a diode for both, then only a single diode is required if a 3rd row signal is provided. This is possible because this system uses SPDT relays, so we can get the desired signal at the input of the last demux, instead of the 2 outputs.

Some deeper analysis will be required to find the optimal configuration but this is worth doing, if it can save even 1/3 of the diodes (the prototype is getting very crowded).