I can only say one thing in regard to drilling PCBs by hand, why are you using a jobber drill? What is a jobber drill? A jobber drill is meant for drilling deep holes and thus have a lot of flute length.
So, let me introduce you to something known as a Center Drill. These guys are designed to be rigid and not break which is a perfect application for drilling PCBs.
Essentially you will drill a starter hole and then switch bits to the jobber drill. Most of you will probably be using a #0 or #1 Center Drill. A typical resistor lead is roughly 1/32 in diameter so a #0 should work just fine. Ultimately you should have less broken drills and your production time should be cut, enough though you will be switching tools. These are fine to use in a drill press for drilling PCBs, they will not walk.