Some progress!
My original plan was to use Brucebars, but I forgot about it and then the carbon rods got in the way. I had seen a somewhat similar solution (kind of Brucebars light) in a thread by
@rojo412 using drive-in nuts somewhere. I like the idea, so I tried it. The pressure distribution across the carbon rods shouldn't hurt (but it probably doesn't make any difference at all). Anyway, I was pretty scared because there isn't too much space left at the edge... Next time I'll measure first and try to find ones with a smaller diameter.
First, I pre-drilled with the Forstner drill bit, then made a pilot hole so that I knew where to drill from the bottom, then drilled the hole for the shaft of the nuts with a 7.5 mm / 0.29 in drill bit, and finally drilled the 6 mm / 0.235 in hole from the bottom.
Next, I filed down the carbon rods a little where they collided with the nuts and then made wooden caps out of veneer to cover all up.
Next I wanted to drill the holes for the tuners. Luckily, I had another look. My plan is to install Graph Tech Ratio tuners. But their axle is over 2 mm / 0.08 in smaller in diameter than the Schaller tuners I have used so far and on the basis of which I determined the position of the holes. So back to square one - aka Inkscape.
After 5 minutes of shock-induced paralysis, I took the fretboard to the router, at least for the contours. Fortunately, this worked without anything splintering. Very gently and carefully. Roasted maple is scarily brittle.