I agree with Mike that taking it to a machinist or gunsmith with a lathe setup is a perfectly reasonable plan.
That said, let me add another detail. I meant to mention that when doing this by hand without a lathe, I think it is helpful to drill the hole 1/8"-1/4" deeper than you want the final hole to be (that is, longer than you want the breach plug to be), and then plan to trim off that extra length and square up the breach before you seat the breach plug. The extra length gives you a little throw-away material to work with as you hand start the tap. This helps because it's easy for the first few threads or so to be a less than perfect as you try to get the tap to grab. Even once it grabs, you often still have to adjust the angle so as to get it aligned with the bore, so the first few threads are often more loosely formed than you want. So, if you give yourself a little extra and plan to trim it, then once it is trimmed, you will have perfect threads all the way to the edge of the breach opening.
Having this extra length for the hole at the beginning also helps you avoid having your starting tap reach too far into the bore. If it reaches too far in, it can scratch the sides of the bore. You have to plan to avoid that.
I hope what I've described is clear.
I use a similar plan when making ramrod tips, and when lock bolts, or jags/worms, or anything with a threaded shank, as well. I make the threaded section just a little longer than needed, and that way I have extra to work with. I'm talking about cutting threads by hand, without a lathe. If the tap or die doesn't start straight, I can work with it and get it going straight. Then trim off that throw-away bit as planned. I imagine professional machinists may have a name for that throw-away margin I'm talking about, but I don't know what it is.