Yes, thats essentially it. The barrel is jigged up and the end mill machines off the now incorrect info, leaving you with a nice flat to re-stamp. The H&Rs are kind of deep, though. A little careful round file work can radius the ends to meet the barrel for a more pleasing rounded transition.
Hand stamping is best achieved with the stamps in a holder to keep in line, but too many characters or numbers can be tough as the impact gets spread out over all of them. A straight guide clamped up can help you keep individual stamps in line. If you try it freehand you will do OK until you dont. Practice on some mild steel first will help. And no, it wont hurt the chamber.
BTW, once you have the stamp held in place, dont watch the stamp end as you hit it, watch the top where you really want the hammer to hit. As you come down on it do so in an arc that if it mis-strikes it will not hit the barrel (or pad up everything, including a glove, to be safe.