Do listen to the speeds here.
You are going to need to turn that drill bit around 10'000 at the slowest. 25'000 would be better.
If you can find an air powered, spindle mounted grinder head, you might get close to the RPM you need. Balance and runout becomes critical at those speeds.
You may just try to mount a pin vise in your BP with a spring type dead center and try drilling those by hand.
That's the way I would go, if it's still in brass, like you said.