I am happy to close this thread by myself because I found the answer here in the following article:
You need to add the following option to the Device section of xorg.conf:
Option "UseDisplayDevice" "DFP"
This seems to be a special option for a Toshiba internal LCD display.
The newest legacy driver - even beta version - works like a charm now!
But it really was hard to find!
Yes, treasure hunting takes time!