Here is where I found some chamber dimensions.
http://www.leverguns.com/dimensions/Default.htmDoesn't cover most chambers, but it is a good start. A drill bit that is smaller than the desired chamber is ok for a rougher, but for finishing a chamber, I would rather use the tool for the job, a finishing reamer.
For just lengthening a .357 Mag chamber, you could make a D reamer if you have access to a machine shop and take careful measurements. Google "D reamer" or "half reamer" as there is some information out there on them.
Here is a quote from Mr. Gale McMillan:
"Turn the shape you want on a lathe out of a good oil hardening tool
steel like Ketos. Put it in the drill press and turn it in slow speed
while heating it with a torch. When it reaches a bright red 1550
degrees lift a can of oil up and quench it while it is rotating. This
prevents warpage as it is heated evenly. Then grind it in half being
sure not to over heat it The arc of the wheel will give you a hollow
ground effect which will make stoning much faster. On any shoulder that
is square to the axis has to be backed off so that it doesn't rub. With
care a good reamer can be made that will cut slowly but well. It is not
critical that it be ground exactly in half as long as it is ground at
least in half. If a pilot is used grind only half of the pilot and
leave half to be a guide. -Gale McMillan"
Just go into this knowing full well you could ruin your barrel, or at least have to ream it out to something bigger to remove the messed up region if you are not careful.