The biggest issue with doing it is not to get too deep once you get to the rim. If the factory rim relief is correct for 357Mag, DO NOT even let the rim cutter portion of the reamer touch down in there. In fact, if you want a 'close chamber', have some loaded up rounds with the longest/heaviest bullet of choice and be test fitting it as you ream and are still a good ways from full cutter depth.
Lots of cutting oil, even, two hand/T handle pressure in a straight line down into a well supported and secure barrel and you are good to go.