i had a similar drill project to remove the broken stub of a large stainless bolt from an alloy caliper

bought some brand new HSS drills

started small and slowly worked up the drill sizes always trying to move the hole to dead center

then when i could just see threads appearing through the metal i switched to small diamond bits and a dremel

chinese made diamond tools can be bought very cheaply now and have changed the way i work with awkward metal

was finally able to pick/tap out the corroded stainless threads from the alloy, run a tap through it and it was as good as new with a new stainless bolt