Get an Ease Out bit that fits the hole pretty tight of the bleeded valve.
That might work.

Jim

 

Is this what you're talking about..?

 

I would carefully drill the bleeder out as much as possible and then take whats left out with the easy out. If the bleeder is that hard to turn then the easy out is likely to break off in the bleeder and you are fubar. The easy outs are hardened steel and snap off pretty easily if you twist them with too much torque (don't ask me how I know that...LOL). They are very hard so forget trying to drill one out if you break it off in the bleeder. If you drill very carefully and keep the drill square to the center of the bleeder it will guide the bit. Just go up one bit size at a time until you see the threads start to appear. At that point the bleader should be fairly loose in the hole and the easy out should remove it without too much trouble. Using a little cutting oil can help with the process as well. It works I'v done it a few times.

Good Luck!