When you drill the heads off, the tendency is to grab a nice sharp bit, chuck it up in the drill motor, stick it in screw, lean into it so it doesn't skip out and skitter across your pretty paint, and pull the trigger. Congratulations, you just broke a flute off. Instead, get a gently used bit that is not new sharp. Center the point in the recess with gentle pressure and pull the trigger with some authority. That will get it to start cutting on center without breaking the flutes. If you want to switch to a new sharp bit after you get it going, that works pretty well.
If I have even one fastener fight me, I don't waste my time hammering the bits. I just get out the drill because the chances of success with it are always 100%.