Since I was not satisfied with the result of the embedded autorouter I did it myself. I have never designed a 2-layer PCB, so I used this extra degree of freedom only when I was stuck. I ended up with only two vias, and other transitions were handled at pads when needed.
ZM1332 cold cathode displays are small and not too tall, so I put all components on the back side of the board, leaving only tubes on top. There are no overlapping components, so it won't matter which side I start soldering.
In order to simplify routing I have remapped the outputs of driver IC to actual digits, so this will have to be taken into account in the firmware. The two headers mantain a 0.1" spacing even if they are far apart.
I am really curious to see the resulting boards, and to build them of course! By the way, the size is 10x5 cm.
If all goes as planned, I will publish what is needed to reproduce this project. Fabricator emailed me they should ship on April 7th, 2017. No idea how long it will take to get here!