Thank you all for your many advices!

Things seem to get clear at working better.

I used the RA and DEC marked wheels to test the mount indoor and hopped from one star or messier to the next. I figured out several issues:
1/the RA pulley had come loose (no idea how I let it loose). So that explains why the telescope was far off.
2/I somehow got confused with the coordinates on the planetarium. Switched from ALT/AZ to DEC/RA. Every motion became obvious. I could test meridian flip.

Conclusions: testing indoor is very useful. I got confused because of RA pulley being slippery combined with meridian flip (so values did not match a +/-12h).

So I understood a lot of things, and on the side why people say Howard is always right.

I will test more, especially the limits to avoid axis motors collision.