Deepening a chamber and rechambering for a different cartridge are two entirely different things. When chambering for a different cartridge, the reamer is not well supported and aligned. There is a tendency to push a little too hard and set up a chatter. Regarding the use of a hand drill or a drill press, I have known guys who did both, with decent results. Just because something is possible though, doesn't mean it's a great idea!
If I was going to ream a chamber by hand, without removing the barrel from the action, I would make an extension, which was a close fit in the receiver, to provide some semblance of alignment.
If I was going to ream a chamber by hand, without removing the barrel from the action, I would make an extension, which was a close fit in the receiver, to provide some semblance of alignment.