some opinions are not impossible, just more steps needed, not easy as to do as a standard per-programs CNC step .
I have asked them to done some CNC option without screw holes, they charged $10 ~25 to do it and said they rather do it manually.
I have done CNC myself, so I knows to not cut some holes , it just need to remove some g code, although it can be done as easy as use a text editor, but to ensure it got no errors as you don't have a seconds chance, as part of my day jobs is production management, I know this kind of cases needs to done a test run for confirmation, so that need time and labour + material cost, so if that just one off requires, I understand they rather do it manually.
so I believe you can ask by email, they can do it at some cost likely by manually.
as they use a vacuum to fix the body for CNC, back of the body may not easy to fix as pickups route already been cut on other sides.