The 4th axis isn’t something covered in the CNC class and not broadly available to members.
This use case for the 4th axis may be doable, depending on your knowledge of Fusion CAM. It’s probably not going to work in VCarve with the current limitations of our controller / gcode interpreter.
The OpenBuilds part store might be of interest, e.g.:
They have a lot of designs/plans, mostly oriented around diy CNC routers. Although it looks like they are shutting down . The designs might still be helpful.
A grbl shield with an arduino is a good choice for this diy project. you could also get away with a belt drive system to save on some cost over a ball screw. all these choices depend on how much you want to spend and what your other goals are for the project
I’m not sure if you’re going to keep making cues, if you are you’re investing your time in the wrong equipment. Look at this videos pay attention at the kind of lathe. The inlay and finishing techniques of this guy are insane. If you look at his videos you learn techniques, repairs, design, and modifications to normal equipment. Anyway, you need a metal lathe in my opinion (in Asmbly they will not let you use theirs for this.