With the 1941 Southbend I use,the last .0001 doesn't matter so much,maybe.
But,I have a 4 screw spider on the back end of the spindle,and a 4 jaw chuck.
I also have two indicators available,and sets of pin gages.
I don't "spend my life" to get Total Indicated Runout inside .0005 both ends
I'd guess about 15 minutes or so.
I bought a floating reamer driver from Elliot Reamers...simple,but it works.
But a commercial die is not a barrel.A die will be harder than woodpecker lips,and you'll just mess up a reamer.
OP,you might go to MSC's site,and search for "brass lap" or "barrel lap"
The "barrel" part is not about rifle barrels.Its about barrel staves,like whiskey barrels.
They have a steel mandrel,with a piece of brass tube the appropriate size attached.The brass is split,like a collet,and there is an adjusting screw the makes the lap expand.
You charge the brass lap with abrasive.Diamond,silicon carbide,or aluminum oxide.
Diamond is nice but expensive.Silicon carbide cuts aggressively but may not leave as fine a finish.Aluminum oxide is probably the stuff I'd use.
Some kerosene or diesel for supplemental lube.
I'd probably set it up in a Bridgeport in a vee block instead of a lathe,easier to stroke in and out with the spindle.
Those laps are not to spendy and work pretty good for .001 or .002.
They would do throats on a wheelgun OK.too.
I know this will bring a gasp of disapproval,but I have patiently cut a chamber with a barrel vertical in a vise,holding the reamer with a tap wrench,turning it by hand.Let the pilot follow the bore,the trick is to apply rotational force without applying side force.If you can hand tap through 1/4in of stainless with a 2-56 tap,you can do that.Keep turning clockwise to back out the reamer.Tap handle has to be tight My results were fine.