Remove the crown and stem and tape off the case tube. I'd start with 320 grit wet/dry and then go to 400, 600 and finish up with 1000, maybe. They make 1500 and 2000 wet dry sandpaper also for finer finishing.
Plan B is to remove the crown/stem, the movement, and the case tube. Then use files to trim the insides of the crown guards and sandpaper to finish and maybe polish. Then tap the hole- 3.0mm x .35 tap and install a new case tube- 6330 and a new crown- 603 or 604. The Bivintage crown and tube aren't the best so this is a nice upgrade- a little more involved but it yields a better assembly.