I breeched barrel by hand, with hardware store tools too. I was young and enthusiastic. The result was poor. The tap drill will chatter in the bore. The hole will not be straight with the bore. The tap will start crooked to some extent. It may end up really crooked, threads may be missing. The tap has a center hole in the drive square for a reason, to guide the tap. The end of the tapped hole will be crude and not smooth. Now you make your plug. The threads will be crooked. You have no material to guide the tap wrench, the plug is to short. When fitting the plug to the barrel it will be cockeyed unless you to an especially sloppy thread fit. The rough chattered internal shoulder and will will not make a good seal with the plug.
I am not saying you can not do it. I am not saying it will be dangerous to shoot. For my sensibilities it will be a makeshift job and that is not how I do things today.
OP, heads up, if you plan on hiring a machinist to make parts for you, forget it. The cost will be huge. An ordinary machinist will not have gun making experience anyway. Save yourself some grief (and money), get a kit. Build it, maybe a few more. Learn the process, then strike out on your own.
If possible do as I did, find a mentor.