Houston we have the Solution!!!
That incredible feeling, when something is working after 5 hours of hassle... :)
So the appropriate thing was to get the amd driver for AHCI (because there was no Gigabyte's own) and installing it. After that, the workaround works. I adjusted the the setting from 3 to 0, then made it to boot in safe mode and Vóila!
Once again, there's not enough words to describe the thankfulness to this Tek-community!
Didn't even have to reinstall :) :) :)