Desktop Lamp Base

The desktop lamp (also known, impropertly, as Pixar lamp) holder is a piece that often gets broken.
I hope whis design will help old and new desktop lamp to resume to life!
This is made around a lamp bought on Amazon, the little metal insert that goes into the holder has a diameter of 12,5 mm. The screw diameter is 5,5 mm and at least 50,0 mm high. Let me know if you need different measures. I plan to make the same design for the Ikea copy of the Naska Loris desktop lamp too.
Open to sugge