Cylindrical Slide Rule

A printed version of a brass slide rule (that I keep in my car to calculate gas mileage) I made previously. I'm having trouble coming up with a good way to join them. Ideally, I'd like the joining to be done with one piece that still allows for a hole in the middle, like with the brass version, but I didn't like any of the ideas I came up with. Please help / derive.

Update: I came up with a center piece that I'm happy with. As I am currently CAD-less, my friend J. Ferrari did the CAD work for the center piece.