I cut the pmma on my Sorotec BasicLine with a 4 mm single flute endmill. Making fast shallow passes and adding some liquid (water/methylated spirits) works very good, still the chips are really messy. Next step was to polish the sides. Then I milled a mold from cheap wood, where I mounted the hanger. I put it into the oven at 170 °C for a good 10 minutes. Then I put it out and bend the part with gloves.
The inner assembly was printed on a Creality Ender 3 with white PLA. I was glad that the screw worked right away. Keep in mind that you need to print the tappet twice.
Because nearly 30 mm of material is pretty hard to cut on a desktop cnc I went with gluing up three layers of 9,6 mm material. I nested the parts exactly with gaps of 3 mm to save some cutting.
This super simple design of a toilet roll holder is a screw-no-glue design for flat-pack shipping and easy assembly. The removable part has some magnets to snap in place. I did resign on a rounded part in favor of a more simple machining process.