Cgs synth

Should I try to switch the cables going to UD and SW and see what happens ?

You could, or add another 47k in series with the switch and see if that helps.

Regarding the reset issue in reverse mode, I checked the parts you said, the 547 is placed following the silkscreen, the associated diodes are placed correctly and behave normally when tested. I have no way to test the pinout on the transistor though (my transistor tester doesn't work any longer apparently). But it comes from the same batch than the 8 others controlling the led and gate outputs, which are behaving correctly, so I doubt the problem come from it. I also tried to swap it for another 547, but with the same results

Try a different chip. Look for soldering problems. Make sure a pin of the chip isn't bent underneath. When in DOWN mode, the chip's PRESET function is used to load the counter with HIGHs (i.e the eighth step in binary).