So I came up with this very rudimentary idea and did a very quick and dirty job. I made 3 spacers, each ca 3mm thick and glued 2 wooden sticks into one of them and only drilled the rest. Each spacer adds ca. 1 degree tilt to the Sharpmaker. Depending on what side I apply them, I can get sharpening angles from 12 to 23 degrees:
Here I have measured the angle of the rod in its 15 deg position with 1 spacer at the opposite site:
I am surprised but it actually works

