What I do is to run a regular nut down the threads first, so it gets turned over the hole after drilling. Doesn't seem to me that you would need to do that if you were using a die to clean up the threads, as the hole will not be at the very end and the die will easily pick up the original threads.
I've done "Grade 8" with just ordinary "cheap Chinese" drill bits, and they seem to cut fine. But I do always use a drill press, with a vice, and a good cutting oil, so YMMV without those things. Gonna be hard to do freehand and keep the hole well enough centered that it will match the slots in the castellated nut, IMO.
What works for me is to take a Dremel with a small round grinding stone mounted, and touch the threads where I want the hole. Gives a nice, smooth place for the drill bit to bite in and not wander. Also makes it easier to line the hole up in the center of the bolt by eye.
But usually, I just buy a matching Nyloc or similar "prevailing torque" nut and don't worry about a hole. Those "deformed thread" nuts work quite well.