I would say if you want to carve necks, then there are some cutting forces to contend with where a screw can have an advantage. I think which ever way you go, it will need work. Luckily for you, YOU HAVE A CNC of which you can cut parts with! You have to design you parts within the accuracy of your machine but it's not out of the realm of possibility. And likely you're going to have to do the leg work.
If you use ballscrews, my biggest concern would be, being the machine is enclosed, ballnut contamination with dust. You'd have to ask for matching sweeps, but they don't really work as well. They make bellows for the screws but they take away some travel. Maintenance, mainly preventive, is key.
As far as tolerances. The instructions quote a tolerance of about .005", which is due partially to the mechanical resolution of the drive system, but also the components and materials. You have to ask yourself if investing in screws with more than double the suggested tolerance than the other parts in the machine are worth it? Likely you won't see much advantage unless you also upgrade to linear rails. Also remember the fixed and free end bearing blocks needed, some form of alignment and shock absorbing couplers for the motors with the requisite proper motor mounts... Your Momus will no longer be. You may want to investigate getting higher quality pulleys and belts with a more accurate tooth profile designed for more precise automation, like GT3...
ACME screws can have a tolerance from .004"-.009"/ft. It may sound like a lot but in practice I found the tolerances are not that bad. Delrin anti-backlash leadnuts can be had rather inexpensively from vendors like DumpsterCNC, the quality is very good, and they last a long time. I've had the same nuts on my machine for over 6 years, with no appreciable signs of wear or lash. You can "tweak" the settings in Mach3 for more accurate results, but I find them fine as-is. Buy them from a reputable source; they have to be precision ACME screw. A 2-start, 4tpi (as in turns per in) would be a good choice and balance of speed and resolution (1/2"-8, 2 start or 1/2"-8, .250" lead is what it would be called out as from a supplier.) You'll have lower rapids, but better torque and resolution at cutting speeds.