Ok, I can tell you the secret to success. It may seem simple, but the key is to never "crowd" the drill. And by this I mean clear the chips more often than you think you need to. After center drilling, Use the best (maybe brand new) drill you have which is the size you want to end up with. Go as deep as you can with it. Then switch to the longer drill. Of course it's nice if its been properly sharpened, but by this time it will want to follow the hole that you've already started. What will make the drill "walk" off center is applying too much pressure, and not clearing the chips often enough. To guarantee success you need to clear the chips every 1/8 of an inch you drill, I know it seems tedious, but it will work. The only reason I would turn the work around is if I didn't have a long enough drill.
I've successfully drilled 1/4 inch holes through solid steel a distance of 24" using this method. I've also seen the same job screwed up by someone who didn't have the patience to back off a little.
Levi