Thierry, maybe I am repeating what you already know very well, if so - sorry.
WRD - as Joe said, it cannot lock the rack, but it influences it to increase fuel when engine is cold. The simple first thing here to test if WRD is responsible for rich condition is to check if it "switches itslef off" when engine is warmed up. You do it either by listening to the air loud noise as it is sucked through the little filter on the WRD (the noise must stop when engine is warm) or you unscrew the filter and feel with your finger if you get suction through the opening. If the device sucks air with warm engine - the WRD may not work ok and cause rich condition. Then there is the whole procedure with shims.
Barometric compensator - if it is broken it usually causes lean condition, bu for instance mine was stuck in the "up" position making mixture rich. Some reading here:
https://www.sl113.org/forums/index.php?topic=12175.msg82217#msg82217I think you may also have cold start solenoid on FIP - but I have not studied how to test it, so I do not know, sorry, my FIP has no solenoids.
Adjustment idle: just to make sure we have it correct - the knob outside (do not turn it while engine is running!) is just for idle, i.e. up to 1500-1700rpm more or less. Clockwise - richer, counterclockwise - leaner.
Adjustment full range: this is another adjustment we may decide to touch while carefully noting down the number of clicks towards each side. It is the screw in the back in the top right corner of the back plate of the pump. It adjusts fuel in the entire range of rpm. Clockwise - leaner (!!), counterclockwise - richer (!!). you can try this one if you are not afraid. You will need small flat screwdriver.
What we cannot touch, I think, are the partial load screws, light and dark, located next to the idle screw. What we also cannot touch is the linkage lever on the pivot at FIP.
Good reading as well:
https://www.sl113.org/forums/index.php?topic=28224.msg203581#msg203581Hope I am not adding confusion....