In your opinion, what is the right thickness to put under the center pin to balance the keyboard; is it better to decrease it to the bare minimum or increase it? What does it affect, if anything? (For pianoexpert) (Can I ask you with what thickness you get better results in the Renner model you used?)
It seems to me that you want to know which thicknesses should be used to level the keyboard by acting on the center bar of the keyboard. First of all, one must know at what height from the keybed the white keys should be leveled (generally 62-64 cm). Some keys at the ends will be leveled and two wooden blocks will be placed under them to prevent them from lowering. This way we can position a perfectly straight metal rule and level the other keys. Increasingly thinner shims will be used until reaching 0.05mm. Note that not all manufacturers level the keyboard according to a straight line (Steinway).
Good luck with your work
P.S. the most commonly used thicknesses: 0.20-0.10- 0.05