Way too much overthinking going on here as usual. There is a big clue in the question “high carbon steel with induction hardened teeth”
I would not use anything special to drill a bit of gauge plate or silver steel so why anything fancy or even spark eroders for this bit of carbon steel.
Get out the armchairs and give it a go.
Bog standard HSS 1/16″ drill that is past it’s best and in the rough work rack and a bit blunt, equally rough Naerok drill press, a bit of Sulphur containing CT90, no punch mark to start it and no skidding about. What could be easier. Hardest thing was holding the springy blade down, holding the camera and pulling the quill down with just two hands. Not even a bit of smoke to make it look like it was hard to drill