A CNC router will certainly cut any angle you can imageine. Problem is the head usually won't rotate, so anything other than a straight up and down cut has to be done with an angled router bit. LABs certainly do not standardize on one angle, so you'll probably end up buying all different angle bits for the CNC company. Fortunately, they last a while and you'll be able to use them for future builds.
Most shops charge CAD time to move the plans into their proprietary router software, and then actual router table time. You can have them buy the wood or provide your own, but expect the final labor of cutting to be around a couple hundred dollars per sub.