Yeah, a drill press works for me too, BUT it's not really as simple as described (at least for me).

The drill BETTER be sharp.
And the cutting speed BETTER be FAST.
And I use a press vice to hold the prop square and give it some mass.

With the press OFF, bring the drill down and to the hole. Turn it backwards by hand to get an rough idex to the hole to set the vice location.
Turn it on and take a very, very small cut. That will give you a very good look at your centering. True up the centering if needbe. Take another indexing cut and true if needed.

That works for me.