The barrel will be just as accurate, for a while, if you just file it completely flat and smooth, at right angles to the bore axis. All that matters is that gases don't exit on one side before the other, and the muzzle doesn't scrape a bit of metal off one side. Either of these will cause the bullet to wobble in flight.
The reason muzzles aren't flat, is that a trifling knock can burr over one or two of the lands. I use a ball-shaped tungsten carbide burr of about 1in. diameter (it could be down to 1/2in. for a small bore.) But I don't use it in the drill, for it can easily wander to one side, and so can the screw and grinding paste, if you accidentally apply sideways pressure. The Brownells tool has a pilot rod to fit the bore, and keep it aligned.
What I do is to hold the burr in a vice, or a hole in a doorframe etc. I then rotate the barrel against it, equalising the cutting effect around the edge of the bore. About 1/32in. deep gives all the protection you need.