Printed one set in clear PET at about 200 °C and 79% infill. The upper holder fits perfectly, which is great! The lower piece, however, has a too small bore. I measured 17.8mm after cleanup. Although I have chosen a 1.2mm perimeter on the print, this might be too much to bore it out to 20mm. Printing it with a bigger diameter might be a better idea here.
The other picture shows the rough dimensions of the PROXXON FBS 240/E. On the grip it has about 47mm diameter (bigger diameter, oval shape, not round). The PROXXON tool is less noisy than the Dremels I think and the instruction says that it's built for continous use. I've been using it on my small DIY CNC and it was fine. The bearings are supposed to be replacable easily and cheaply.
Update: I've sanded the hole in lower clamp to 20mm. It's a tight fit and the mount seems to be very stable!