The Ring Joey did above is unique, it I am sure to get everything matched up perfectly take a lot of time.
Machine work with wood is tougher than steel. Wood can be tough because constantly changing density.
Steel, Aluminum, and metal are the headaches natural materials are.
You could, for example, machine slots on the ID of your ring billet and use those to align your ring sections on the cue.
By no special machinery, I mean nothing that wouldn't typically be in a cue maker's shop. Of course, machining a groove on the ID wouldn't be a typical operation, so you would have to come up with a setup to do that.