The crowning tool is not intended for long cuts or under power, it's for squaring up the muzzle to the bore centerline while turned by hand
Cut the barrel to 1/16th of an inch or less from the final length, then use files and a good square to square it up. Chuck a slotted dowel in a drill with 120 grit wet or dry abrasive paper to deburr and polish.
Since I'm cheap, I would fit a short 3/4 inch dowel to the bore. Drill the dowel for a 1/4 inch bolt with the head cut off. Put that assembly through a hole in a flat piece of oak scrap as perpendicular as feasible. Glue a piece of abrasive paper to the face, then chuck the tool in a drill and finish the crown.
A friend with a lathe could knock out a beautiful tool in just a few minutes. I can think of all sorts of variations and possibilities for squaring, deburring, and chamfering tools that would not cost much.