You can try and make your own hole/core drill. A copper or brass tube the dia. you need you cut 4 or 6 slots in one end about 4 to 6 mm(3/16 to 1/4 " deep. You will need to remove glazed or vitrified surface the size of hole. The diamond burs work well.
You then make dam around the hole site, mix up a slurry of oil and grit, either some rock polishing grit or blasting medium to fine silicon carbide grit any light to medium weight oil will do. The slots trap some grit and slurry and with a slower speed and light steady pressure. It cuts through the pottery beneath the glaze.
The spade looking bits are called tile or glass bits on this side of the pond. The claim is that the points start the hole by chipping the glaze away. I always have had better luck pre starting them with a diamond burr, carbide burr or even a pointed grinding stone used wet of course.
Can't see why your mill if it is like most drill/mills can't be used. I would suggest that you get a can pan large in dia than the plates to contain the spray/splashing. On occasion I have taped some card stock extending above the pans rim to contain spray. I had one about 30 cm's(12") in dia with a rim about 40mm (1 1/2" tall)
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