rae comments about a clutch was relevant, since I'm pretty sure that my drill doesn't have any sort of clutch like that. With those cutters, it's pretty much a given that they are going to stick along the way, if only a bit, and it's going to damn well hurt!
I suspect I'll do the lots of little holes approach, since I've got all that I need already. I may need to do this again, since I've got a cunning plan to run a vent in for the cooker hood, but I still think it's not worth buying more expensive kit, since this would probably have to include a new drill!