It's too late but the following idea struck me at the last moment of routing.
There is actually no need of two common rails for the display. One rail that is switched from 0 to +Vcc is enough. This would simplify the routing, though in this case, the difference is not important enough to justify rerouting anything. I'll leave it like this but I write this as a "reminder for later".
For now, the system works like this : each Flash pin goes to a resistor then two LEDs, each tied to one of the common rails. The LEDs are wired in the same direction so one of the rails must be set to 0V to turn the corresponding LED on.
This is actually overkill if we realise that the LEDs could be connected in reverse and in parallel, with the single common rail swinging for 0V (to turn one LED on) to +VCC (this turns the other LED on). The only change is to reverse the value of the FLASH memory for one half of the output values.
This becomes more complex since the 5th digit's decoder would require a total redesign as well...
This did not work as expected. But all is well that ends well !