I can understand your problem David, you go slow drill with your press drill and diamond bits, for your purposed to drill with, you allready got best choices, but yes it's high cost as you will toss your bits very quickly, not mention time you took.
I did this way too to cut a mass in the middle of slab, but not on a thick slabs, usually slab will go spin like crazy when your bit passed trough slab and you will broke it or wound your hand.
Cut slab into round flat first and start grinding is most efficient, precission is the next issued with this way.