It would be nice though to then safe the gathered values and keep them even after reboot. Is this possible?
Yes, there are ways of saving values in non-voltatile memory. But I don't see the point, since the controls can move during power down.
I do not want to save the latest input values but the extreme values of each pot as well as the central position value of each pot, after the calibration routine.
I would like to know why you think a calibration routine, like windows did it before self calibrating hardware was available, is a bad idea?