'Dormer' are probably one of the best you can get, although even their quality isn't what it used to be (cue for a song). Cobalt tipped ones are also good.
It is possible that you have hardened the screw by having the drill bit spinning without cutting, and generating heat. If that is the case you will need a good quality, sharp drill bit and use it with a firm pressure and medium to low speed. Not easy with a pistol drill when you're working positionally, and please don't slip
