No machines are necessary.  Speaking from experience on doing a 357 Max   
With the Chambered Barrel in place, try a case.  It should go in a bit.  Now for the fun, take a Magic Marker or Machinist Dykim and coat the Groove.  Try to feed the round and see where the marking has been rubbed.  I used a 3/4" grinding stone by hand to remove the marked area.  And then do it all over again. I found that it was the outside edges that needed opening up rather than the depth.  Took me about 3 hours, surprised me, to get the case to feed.  But then again what else is there to do on a Cold Winters Night in the middle of God's Country.
Good luck,. David

Myself and only if enough there is enough room to do such a task. I would use the appropriate sized ball end mill and only after having it completely indexed correctly. In a mill vise while also doing the work on a mill. We are now the care takers for some if not all of these old per-say rifles To me if not doing it completely right one would no longer be the right care taker for such rifles.

Could try taking some off the rim diameter and see if that works first.

Way to go👍🏻