Updated the mount to allow room for swivel. The arm would hit the corner before, now it should clear it.
The C270 camera mount is attached to the camera using it's own hinge pin. The dual diameter bolt fits through the sliding mount. To remove the original weighted Logitech mount from the camera, use a thin knife to remove the covers over the ends of the hinge pin. You should then be able to use a screwdriver to remove the pin. You may need to push the pin out with a thin screwdriver or similar tool. The printed camera mount will be loose on the hinge. Use a small (M3?) metal washer at one end of the hinge pin, and a very small rubber washer at the other end of the hinge pin.
Here is a video of the disassembly process https://www.youtube.com/watch?v=bWz1-wV8AU4
I also made some small improvements on the arm itself. I increased the diameter of the top hole to accommodate the spring. Otherwise there wasn't enough room to lower the bed enough for proper leveling.
Since the bed of the CR-10 is so large you might want to get a larger field of view. I achieved this by using this adapter https://www.thingiverse.com/thing:1253022 and some cheap cell phone lenses off of amazon.