In the end I want the CNC to finish the complete neck... I might want to touch it up with sandpaper, but all machining must be done by the machine.
Right off the bat I highly doubt you will ever get one right off the machine that only requires a bit of sandpaper touch up using a rotary axis. I could be wrong, but I would be willing to bet a 12 bucks against a dozen donuts. No wait, I do not need to eat a dozen donuts! The last time I looked it was not possible to cut across the centerline of the model. Translation, the centerline of the model had to have material all around it. No cutting below centerline.
I think you can do the whole thing on the cnc, just not with a rotary axis. If'n it were me, I would create fixtures for the various positions required. Custom cut, not just jury rigged with a couple of dowel holes. What is nice about a cnc is that we can cut those kind of fixtures pretty easily. I would have one that would hold the neck so the tuning box cut out was accessible (fixture the neck at an angle). Not sure if you can do this on your machine, but I can cut beyond the front of my machine for about 4 inches so I can do end work and weird angle stuff when need be.
Quite often I will set up several fixtures on the machine for something I am doing. The workpiece offsets are a real savior with multiple fixtures on the table.
Sometimes we waste a lot of time trying to make something happen a certain way when it would be easier to just step back and say "wait a minute, am I looking at this correctly or am I kidding myself?"
Just my thoughts. . . .
A footnote: On my table I drilled a bunch of holes for dowels in a pattern, they are on two inch centers. So what I do is drill a base piece with a set of matching holes. Then I fasten the base piece to the machine. Then I fasten the material I am going to use for the fixture to the base itself. That way, if I screw up machining the fixture I can just replace the upper material. The dowel holes make locating the fixture on the table easy if the fixture is removed. All of the fixture cuts are referenced from the dowel holes. Takes a bit of thinking but it works extremely well. Beki did a version of this in one of her videos. She cut a block to hold the material rather than using the dowel hole method. I recently did it on a full 3D model. I cut the first side to the halfway mark, then cut a negative of that in a block to locate it so I could the backside and know it was located correctly. That way I did not need to leave material attached to hold the work.