Hoooooooray! 
Found what was the last issue. I just thought about this other righthanded model subject (here: Models are reversed when put in a parent) and realized thta if the scale was reversed, then the position should too!
So when I set the center, I just take the negative value on x and y axis as for the scale this is the z axis which need to be negative and BOOOOM, it works!
Thanks @Deltakosh for leading me to the solution! Here it is: https://www.babylonjs-playground.com/#0108NG#23