I recently built an X-carve CNC machine. Being a former woodturner I can see some neat appllications for the CNC with a 4th axis for lathe rotation. From what I have seen such additions are expensive.
But… An Eggbot might be capable of suppying the needed rotating hardware and with appropriate software its stepper motor might do the rotation job. Much of the CNC software is capable of controlling the 4th axis stepper.
I am not in a position to do anthing yet, but having both the X-carve and your Eggbot (mine is not the fancy new one) causes one to think abouta hybrid.
We have thought about this previously in the context of using the EggBot as a rotary axis in a laser. (It should work but we haven’t gotten around to it– mainly for lack of actually needing to laser any round objects.)
My main concern would be that the hardware isn’t designed to resist the force exerted by a cutting tool. The bearings are light duty, and there is some slop in the tailstock bushings. So, you might need to beef it up a bit, or machine equivalent fixtures on the X-carve.